Rivers v. Guerrero

Opinion of the Court

Ketanji Brown Jackson

PRELIMINARY PRINT

 Volume 605 U. S. Part 2
 Pages 443–459

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 THE SUPREME COURT
 June 12, 2025

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 OCTOBER TERM, 2024 443

 Syllabus

 RIVERS v. GUERRERO, DIRECTOR, TEXAS DE-
 PARTMENT OF CRIMINAL JUSTICE, COR-
 RECTIONAL INSTITUTIONS DIVISION
certiorari to the united states court of appeals for
 the fth circuit
 No. 23–1345. Argued March 31, 2025—Decided June 12, 2025
Petitioner Danny Rivers was convicted in Texas state court of continuous
 sexual abuse of a child and related charges. After unsuccessfully seek-
 ing direct appeal and state habeas relief, Rivers fled his frst federal
 habeas petition under 28 U. S. C. § 2254 in August 2017, asserting claims
 of prosecutorial misconduct, ineffective assistance of counsel, and other
 constitutional violations. The District Court denied the petition in Sep-
 tember 2018, and Rivers appealed to the Fifth Circuit, which granted a
 certifcate of appealability on his ineffective-assistance claim in July
 2020.
 While his appeal was pending, Rivers obtained his trial counsel's cli-
 ent fle, which contained a state investigator's report that he believed
Page Proof Pending Publication
 was exculpatory. After the Fifth Circuit denied his request to supple-
 ment the record on appeal, Rivers fled a second § 2254 petition in the
 District Court based on this newly discovered evidence. The District
 Court classifed this second-in-time fling as a “second or successive”
 habeas application under § 2244(b) and transferred it to the Fifth Circuit
 for authorization to fle. Rivers appealed the transfer order, and the
 Fifth Circuit affrmed, holding that the fact that Rivers's frst petition
 was still on appeal did not permit him to circumvent the requirements
 for successive petitions under § 2244 as to his second fling.
Held: Once a district court enters its judgment with respect to a frst-fled
 habeas petition, a second-in-time fling qualifes as a “second or succes-
 sive application” properly subject to the requirements of § 2244(b).
 Pp. 450–459.
 (a) The Antiterrorism and Effective Death Penalty Act of 1996
 (AEDPA) contains several signifcant procedural barriers that strictly
 limit a court's ability to hear “claim[s] presented” in any “second or
 successive habeas corpus application.” §§ 2244(b)(1), (2). Relevant
 here, § 2244 prohibits habeas applicants from fling a subsequent petition
 that relitigates the merits of previously denied claims. See
 § 2244(b)(1). Even if the subsequent petition presents a new claim, the
 second-in-time application can only proceed if it “relies on a new and
 retroactive rule of constitutional law” or “alleges previously undis-
444 RIVERS v. GUERRERO

 Syllabus

 coverable facts that would establish [the petitioner's] innocence.” Ban-
 ister v. Davis, 590 U. S. 504, 509 . In addition, a petitioner cannot
 bring a second or successive habeas application directly to the district
 court but must frst go to the court of appeals and make a “prima facie
 showing” that the petition satisfes one of § 2244(b)(2)'s exceptions.
 Pp. 450–451.
 (b) The Court has jurisdiction to review this dispute. Respondent
 contends that Rivers lacks standing because the Fifth Circuit has now
 affrmed the District Court's judgment denying the initial habeas peti-
 tion on the merits. But because a favorable decision here would re-
 dress Rivers's alleged injury that the District Court inappropriately
 transferred his second habeas application to the Fifth Circuit for review
 under § 2244(b), Rivers has appellate standing with respect to that legal
 claim. Nor does the fact that Rivers is no longer in custody on the
 child-pornography conviction that his second habeas fling challenges
 defeat this Court's habeas jurisdiction, given that Rivers remains incar-
 cerated on related sexual-abuse sentences that the newly discovered
 evidence may implicate. Pp. 451–452.
 (c) The phrase “second or successive habeas corpus application” in
 § 2244(b)(2) is a “term of art” that does not refer to all habeas flings made
 second in time following an initial application. Whether a fling qualifes
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 as a second or successive application generally turns on the existence of a
 fnal judgment with respect to the frst petition, not the status of any
 appeal. An amended petition fled before judgment is not second or
 successive because fnal judgment has not issued, while a motion under
 Federal Rule of Civil Procedure 60(b) fled after judgment counts as a
 second or successive application if it attacks the court's previous resolu-
 tion of a claim on the merits or seeks to add new grounds for relief.
 Rivers's argument that his second fling should not trigger § 2244(b)
 because his appeal was pending is unpersuasive. The Court's decision
 in Banister v. Davis, 590 U. S. 504 , does not support a rule that is based
 on appeal timing but rather confrms that entry of fnal judgment gener-
 ally separates frst from second or successive habeas flings. Rule 59(e)
 motions present a unique variant because they suspend fnality and help
 produce a single fnal judgment, but Rivers's fling does not fall within
 this narrow category. Pp. 452–454.
 (d) Purpose and history do not support Rivers's interpretation either.
 Section 2244(b)'s restrictions aim to conserve judicial resources, reduce
 piecemeal litigation, and lend fnality to state-court judgments within a
 reasonable time. Drawing the second-or-successive line at the end of
 appellate review would allow petitioners to fle numerous new applica-
 tions during appeals, prolonging cases and encouraging piecemeal litiga-
 tion. Historical habeas doctrine before AEDPA was inconsistent re-
 Cite as: 605 U. S. 443 (2025) 445

 Syllabus

 garding treatment of new flings during pending appeals, providing no
 clear guidance. Pp. 454–457.
 (e) The Court declines to address Rivers's alternative argument that
 his second fling, which he argues was a Rule 15 motion to amend, is not
 a new application by its nature. This theory was not presented in the
 petition for certiorari or to the courts below and makes its frst appear-
 ance in the merits briefng. Additionally, the factual predicate is lack-
 ing because the District Court lacked jurisdiction to grant such a motion
 while the case was on appeal, and Rivers never requested an indicative
 ruling under Rule 62.1. Pp. 457–459.
 99 F. 4th 216 , affrmed.

 Jackson, J., delivered the opinion for a unanimous Court.

 Peter A. Bruland argued the cause for petitioner. With
him on the briefs were Virginia A. Seitz, Benjamin M. Mun-
del, Cody M. Akins, and Jacob Steinberg-Otter.
 Aaron L. Nielson, Solicitor General of Texas, argued the
cause for respondent. With him on the brief were Ken Pax-
ton, Attorney General, Brent Webster, First Assistant Attor-
Page Proof Pending Publication
ney General, William F. Cole, Principal Deputy Solicitor
General, Jacob C. Beach, Assistant Solicitor General, Joseph
P. Corcoran, Deputy Chief, Criminal Appeals Division, and
Lori Brodbeck, Meagan Corser, and Justine Tan, Assistant
Attorneys General.
 Matthew Guarnier i argued the cause for the United
States as amicus curiae urging affrmance. With him on
the brief were Acting Solicitor General Harris, Deputy So-
licitor General Feigin, and Antoinette T. Bacon.*

 *Briefs of amici curiae urging reversal were fled for Former Federal
and State Prosecutors by Joshua D. Branson and Jarrod A. Nagurka; for
Former Federal Judges by Andrew T. Tutt and Dana Kagan McGinley;
for the National Association of Federal Defenders et al. by Jonathan Kirsh-
baum, Shelley Fite, David M. Porter, Rachel Julagay, and David F. Ness;
and for Phillips Black, Inc., by John R. Mills.
 Briefs of amici curiae urging affrmance were fled for the State of
Arkansas et al. by Tim Griffn, Attorney General of Arkansas, Dylan L.
Jacobs, Interim Solicitor General, and Asher L. Steinberg, Senior Assistant
Solicitor General, by Christopher M. Carr, Attorney General of Georgia,
446 RIVERS v. GUERRERO

 Opinion of the Court

 Justice Jackson delivered the opinion of the Court.
 Incarcerated individuals who seek to challenge their im-
prisonment through a federal habeas petition are generally
afforded one opportunity to do so. See 28 U. S. C. §§ 2254 ,
2244. Before a federal court can address a petitioner's sec-
ond or successive federal habeas fling on the merits, the
incarcerated fler must clear strict procedural hurdles that
the Antiterrorism and Effective Death Penalty Act of
1996 (AEDPA) erects. See § 2244(b). This case pre-
sents the question of how to classify a second-in-time habeas
fling when the judgment denying the frst application is
under review on appeal. Does that second habeas-related
submission qualify as a second or successive application,
thereby triggering § 2244(b)'s stringent gatekeeping
requirements?
 We hold that, in general, once the district court has en-
tered its judgment with respect to the frst habeas petition,
Page Proof Pending Publication
a second-in-time application qualifes as “second or succes-

Stephen J. Petrany, Solicitor General, and Justin T. Golart, Deputy Solici-
tor General, and by the Attorneys General for their respective States as
follows: Steve Marshall of Alabama, James Uthmeier of Florida, Raúl
Labrador of Idaho, Theodore E. Rokita of Indiana, Brenna Bird of Iowa,
Kris W. Kobach of Kansas, Russell Coleman of Kentucky, Liz Murrill of
Louisiana, Lynn Fitch of Mississippi, Andrew Bailey of Missouri, Michael
T. Hilgers of Nebraska, Aaron D. Ford of Nevada, Drew H. Wrigley of
North Dakota, Dave Yost of Ohio, Gentner Drummond of Oklahoma, Alan
Wilson of South Carolina, Marty J. Jackley of South Dakota, Jonathan
Skrmetti of Tennessee, Derek Brown of Utah, Jason Miyares of Virginia,
and Patrick Morrisey of West Virginia; for the Commonwealth of Pennsyl-
vania et al. by David W. Sunday, Jr., Attorney General of Pennsylvania,
Hugh J. Burns, Jr., and Ronald Eisenberg, Senior Deputy Attorneys Gen-
eral, Kirsten E. Heine, Executive Deputy Attorney General, Kathleen Jen-
nings, Attorney General of Delaware, and Matthew J. Platkin, Attorney
General of New Jersey; for the Criminal Justice Legal Foundation by Kent
S. Scheidegger; and for Sen. John Cornyn by Owen J. McGovern.
 Igor V. Timofeyev, Stephen B. Kinnaird, Vladimir J. Semendyai, and
Vanessa Omoroghomwan fled a brief for Lee Kovarsky et al. as amici
curiae.
 Cite as: 605 U. S. 443 (2025) 447

 Opinion of the Court

sive” and is thus properly subject to the requirements of
§ 2244(b).
 I
 In 2012, a Texas state-court jury convicted petitioner
Danny Rivers of continuous sexual abuse of a child, two
forms of indecency with a child, and possession of child por-
nography. Rivers unsuccessfully sought direct appeal and
state habeas relief.
 In August 2017, Rivers fled his frst federal habeas peti-
tion under 28 U. S. C. § 2254 , a statute that permits a federal
court to evaluate a state prisoner's claim “that he is in cus-
tody in violation of the Constitution or laws or treaties of the
United States.” § 2254(a). In that habeas petition, Rivers
asserted, inter alia, claims of prosecutorial misconduct, inef-
fective assistance of trial and appellate counsel, and due
process and equal protection violations.
 The District Court denied Rivers's habeas petition, issuing
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its judgment in September 2018. Rivers then invoked the
procedure that AEDPA prescribes for seeking to challenge
a § 2254 habeas denial in the court of appeals: He asked the
Fifth Circuit to give him what is known as a “certifcate of
appealability.” 1 A Fifth Circuit Judge granted Rivers's re-
quest in July 2020, but only as to his claim for ineffective
assistance of counsel.
 While his appeal was pending, Rivers gained access to his
own client fle, which had been in his trial counsel's posses-
sion. The fle contained a state investigator's report that
discussed two computer documents Rivers believed were re-

 1
 Individuals seeking to appeal the denial of a § 2254 habeas petition
must receive permission to do so by obtaining such a certifcate. See
§ 2253(c)(1)(A) (“[A]n appeal may not be taken to the court of appeals from
. . . the fnal order in a habeas corpus proceeding in which the detention
complained of arises out of process issued by a State court” “[u]nless a
circuit justice or judge issues a certifcate of appealability”). A certifcate
of appealability can issue “only if the applicant has made a substantial
showing of the denial of a constitutional right.” § 2253(c)(2).
448 RIVERS v. GUERRERO

 Opinion of the Court

lated to his convictions; one document was labeled “of inter-
est,” while the other was specifcally described as “not child
porn.” App. 94 (capitalization deleted). Rivers promptly
requested to supplement the Fifth Circuit's case record with
this purportedly exculpatory information, but the Fifth Cir-
cuit denied that request. Rivers then asked the appellate
panel to either stay the appeal or remand the case to the
District Court to allow him to present this new evidence to
the lower court in the frst instance. See id., at 99 (arguing
that “justice and judicial economy would best be served” if a
single court considered “all grounds” for relief (capitalization
deleted)). The Fifth Circuit rejected the stay-or-remand
request as well and, thereafter, affrmed the District Court's
denial of Rivers's § 2254 petition on the merits. This Court
denied certiorari. See Rivers v. Lumpkin, 598 U. S. 1234
(2023).
 Notably for present purposes, after the Fifth Circuit de-
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nied Rivers's request to supplement the record, Rivers fled
another § 2254 petition with the District Court. This peti-
tion included the newly obtained state investigator's report
and raised claims for relief related to that evidence. A Mag-
istrate Judge recommended that this second-in-time habeas
petition be classifed as a “second or successive” habeas ap-
plication for § 2244(b) purposes. Rivers objected, arguing
that his second § 2254 fling should not be construed as a new
habeas application. Rather, Rivers asserted, the new fling
should be treated as an amendment to his initial habeas peti-
tion, because the judgment related to that frst petition was
still on appeal.
 The District Court rejected Rivers's argument. It con-
cluded that the second-in-time fling was a second or succes-
sive habeas petition subject to § 2244(b)(2) and transferred
the fling to the Fifth Circuit for a determination whether
§ 2244(b)(2)'s gatekeeping requirements for second or succes-
sive habeas petitions had been satisfed. See Part II, infra.
Rivers then appealed the District Court's transfer order,
 Cite as: 605 U. S. 443 (2025) 449

 Opinion of the Court

again insisting that his fling was not a second or successive
habeas petition (as opposed to a motion to amend) “because
his frst-in-time petition was still pending on appeal.” Riv-
ers v. Lumpkin, 99 F. 4th 216, 218 (CA5 2024).
 The Fifth Circuit affrmed. In its view, “the timing of
Rivers's second-in-time petition d[id] not permit him to cir-
cumvent the requirements for fling successive petitions
under § 2244.” Id., at 221. The panel reasoned that the
District Court could have treated the second-in-time fling
as a request to amend under Federal Rule of Civil Procedure
15 if the judgment relating to Rivers's frst petition had been
vacated on appeal and the case reopened in the District
Court. Ibid. But because the judgment as to the frst peti-
tion had not been so vacated, “Rivers's second-in-time habeas
petition” was a “second or successive” petition that was “sub-
ject to the district court's transfer order for lack of jurisdic-
tion absent authorization to fle.” Id., at 223.
Page Proof Pending Publication
 The Fifth Circuit's decision entrenched a Circuit split over
how to characterize a second-in-time habeas fling that is
fled when an appeal of the judgment of the frst habeas fling
is pending.2 Is the second fling a “second or successive”
habeas petition for § 2244 purposes, or not? We granted cer-
tiorari to resolve that split. 604 U. S. 1041 (2024).

 2
 The majority of Circuits to consider the issue have concluded that
§ 2244(b) applies to a second-in-time habeas fling as of the district court's
entry of fnal judgment related to the frst application, regardless of the
status of any appeal. See, e. g., Balbuena v. Sullivan, 980 F. 3d 619 , 641–
642 (CA9 2020); Phillips v. United States, 668 F. 3d 433 , 435–436 (CA7
2012); Ochoa v. Sirmons, 485 F. 3d 538 , 540–541 (CA10 2007) (per curiam);
Williams v. Norris, 461 F. 3d 999 , 1003–1004 (CA8 2006). The Second
Circuit, by contrast, has held that “so long as appellate proceedings follow-
ing the district court's dismissal of the initial petition remain pending
when a subsequent petition is fled, the subsequent petition does not come
within AEDPA's gatekeeping provisions for `second or successive' peti-
tions.” Whab v. United States, 408 F. 3d 116, 118 (2005) (emphasis added);
see also United States v. Santarelli, 929 F. 3d 95, 105 (CA3 2019) (“join-
[ing] the Second Circuit”).
450 RIVERS v. GUERRERO

 Opinion of the Court

 II
 Habeas petitioners are generally entitled to “one fair op-
portunity” to litigate the merits of their postconviction
claims in federal court. Banister v. Davis, 590 U. S. 504, 507
(2020); see also Slack v. McDaniel, 529 U. S. 473 , 485–486
(2000); Stewart v. Martinez-Villareal, 523 U. S. 637, 643
(1998). When a person seeks to bring a subsequent federal
habeas challenge to his detention, “the road gets rockier.”
Banister, 590 U. S., at 509 . AEDPA contains several sig-
nifcant procedural barriers that strictly limit a court's abil-
ity to hear “claim[s] presented” in any “second or successive
habeas corpus application.” §§ 2244(b)(1), (2).
 Several of those barriers are relevant to the issue pre-
sented in this case. First, § 2244 prohibits habeas applicants
from fling a subsequent petition that relitigates the merits
of previously denied claims. See § 2244(b)(1) (stating that
any claim that “was presented in a prior application shall be
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dismissed”). Second, even if the subsequent petition pre-
sents a new claim, the second-in-time application can only
proceed if it “falls within one of two narrow categories”: The
claim must “rel[y] on a new and retroactive rule of constitu-
tional law” or “alleg[e] previously undiscoverable facts that
would establish [the petitioner's] innocence.” Banister, 590
U. S., at 509 ; see also § 2244(b)(2). Additionally, a petitioner
cannot bring a second or successive habeas application di-
rectly to the district court. Instead, he must frst go to the
court of appeals and make a “prima facie showing” that the
petition satisfes one of § 2244(b)(2)'s exceptions, and that
court has to grant authorization for the petitioner to proceed
in district court. § 2244(b)(3). And then, even when such
leave is granted, the district court must independently con-
firm that the petition satisfies the requirements of
§ 2244(b)(2). See § 2244(b)(4).
 These rules apply to second-in-time habeas flings even if
the fling is not styled as a § 2254 habeas application by the
 Cite as: 605 U. S. 443 (2025) 451

 Opinion of the Court

fler—so long as the document is a § 2254 petition in sub-
stance. For example, a self-styled “motion” that “seeks to
add a new ground for relief ” or “attacks the federal court's
previous resolution of a claim on the merits” can be con-
strued as a second or successive petition and forced to face
the gauntlet of § 2244(b), no matter how it is labeled. Gon-
zalez v. Crosby, 545 U. S. 524, 532 (2005) (emphasis deleted).
 III
 Respondent presents two arguments for why we lack ju-
risdiction over today's dispute about how Rivers's second-in-
time habeas fling should be characterized: frst, that Rivers
lacks standing because his injury is not redressable; and sec-
ond, that the Court lacks habeas jurisdiction because Riv-
ers's child-pornography sentence has expired. For his part,
Rivers makes two alternative arguments about the merits.
He maintains that the second-in-time habeas petition does
not trigger the second-or-successive requirements of
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§ 2244(b) because his appeal of the frst petition was pending
when he fled the second one. Alternatively, he argues that
his second-in-time fling should be construed as a motion to
amend—and, so construed, does not qualify as an “applica-
tion” to which § 2244(b)'s requirements apply.

 A
 We begin our analysis by quickly disposing of respondent's
contention that we lack jurisdiction. Respondent frst in-
sists that Rivers lacks standing because the Fifth Circuit has
now affrmed the District Court's judgment denying the ini-
tial habeas petition on the merits, and this Court lacks the
authority to reopen that judgment in this separate litigation.
But a favorable decision from this Court would redress Riv-
ers's alleged injury—namely, that the District Court inap-
propriately transferred his second-in-time habeas application
to the Fifth Circuit for review under § 2244(b). Rivers
452 RIVERS v. GUERRERO

 Opinion of the Court

therefore has appellate standing with respect to that legal
claim. See Food Marketing Institute v. Argus Leader
Media, 588 U. S. 427, 433 (2019).
 Respondent is also mistaken regarding the contention that
the Court lacks habeas jurisdiction because Rivers is no
longer in custody on the child-pornography conviction that
the second habeas fling challenges. See § 2254(a) (permit-
ting an application from an individual “in custody”). The
record establishes that the newly discovered evidence Rivers
wants the federal courts to consider implicates the sexual-
abuse sentences for which Rivers remains incarcerated, too.
Thus, we retain habeas jurisdiction to review his claims.

 B
 1
 Turning to the parties' merits arguments concerning Riv-
ers's second-in-time habeas fling, we note, to start, that the
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phrase “second or successive . . . application” as it appears in
§ 2244(b)(2) is a “term of art”—that is, it does not necessarily
“ `refer' to all habeas flings made `second or successively in
time,' following an initial application.” Banister, 590 U. S.,
at 511 (quoting Magwood v. Patterson, 561 U. S. 320, 332
(2010)). Instead, the second-or-successive moniker applies
only to “claim[s]” that have been presented in subsequently
fled “applications.” § 2244(b)(2). A “claim,” as that term
is used in § 2244(b), is “an asserted federal basis for relief ”
from the judgment of conviction. Gonzalez, 545 U. S., at
530 . And an “application” is “a fling that seeks `an adjudi-
cation' ” of one of those claims “ `on the merits.' ” Ibid.
(quoting Woodford v. Garceau, 538 U. S. 202, 207 (2003); em-
phasis deleted); see also Gonzalez, 545 U. S., at 533 (explain-
ing that motions that do not “substantively addres[s] federal
grounds for setting aside the movant's state conviction,” for
example, are not subject to the second-or-successive bar).
 Rivers acknowledges that his second-in-time fling “raised
several new claims” that he had not presented previously to
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 Opinion of the Court

the District Court. Pet. for Cert. 12. Still, in his petition
for certiorari—and, to a lesser extent, his merits brief—Riv-
ers argues that this fling did not qualify as a second or suc-
cessive application triggering § 2244(b) because it was sub-
mitted during the pendency of his appeal of the judgment
related to his frst habeas petition. Id., at 24; Brief for Peti-
tioner 37. We do not agree with that proposition. Our case
law establishes instead that whether a fling qualifes as a
second or successive application generally turns on the exist-
ence of a fnal judgment with respect to the frst petition,
not the status of an appeal.
 We have noted, for example, that “an amended petition,
fled after the initial one but before judgment, is not second
or successive” for § 2244(b) purposes precisely because fnal
judgment has not issued. Banister, 590 U. S., at 512 (em-
phasis added). On the other hand, we have determined that
a motion for relief from judgment under Federal Rule of
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Civil Procedure 60(b) (fled, obviously, after the judgment
has issued) counts as a second or successive application if
that fling “attacks the federal court's previous resolution of
a claim on the merits” or “seeks to add a new ground for
relief ” not addressed by the judgment. Gonzalez, 545 U. S.,
at 532 (emphasis deleted).
 Pointing to Banister, Rivers insists that this Court has
already rejected a moment-of-judgment rule for distinguish-
ing between second-in-time flings that qualify as second or
successive applications and those that do not. But our rul-
ing in Banister related to a materially different fling sub-
mitted in a materially different context. There, the Court
considered whether a motion to alter or amend a judgment
under Federal Rule of Civil Procedure 59(e)—i.e., a motion
fled within 28 days that seeks to correct an error in the
District Court's judgment prior to an appeal—should be con-
strued as a second or successive fling under § 2244(b). 590
U. S., at 511 . To be sure, the respondent in that case had
“urged this Court to hold that `[e]ntry of fnal judgment is
454 RIVERS v. GUERRERO

 Opinion of the Court

the dividing line between a frst and second application,' ”
as Rivers notes. Brief for Petitioner 37 (quoting Brief for
Respondent in Banister v. Davis, O. T. 2019, No. 18–6943,
p. 18; alteration in original). But Rule 59(e) motions present
a unique variant to the otherwise generally applicable rule
that entry of fnal judgment separates frst from second or
successive habeas flings.
 Specifcally, unlike a Rule 60(b) motion for relief from judg-
ment, which seeks to challenge an extant judgment, a suc-
cessful Rule 59(e) motion merely “suspends fnality” of the
original judgment so that the district court can “fx any mis-
takes and thereby perfect its judgment before a possible ap-
peal.” Banister, 590 U. S., at 516 . A Rule 59(e) motion is
“a limited continuation of the original proceeding—indeed, a
part of producing the fnal judgment granting or denying
habeas relief.” Id., at 521 . As a result, disposition on a
Rule 59(e) motion “merges into the fnal judgment” of the
initial habeas fling. Id., at 516 .
Page Proof Pending Publication
 In other words, Rule 59(e) motions are “attendant on the
initial habeas application” itself and “hel[p] produce a single
fnal judgment for appeal.” Id., at 515–516. Thus, they are
not themselves properly considered to be second or suc-
cessive flings under AEDPA. Id., at 517 ; see also id., at
518–520 (contrasting this with second-in-time flings that
“collaterally attack [the District Court's] already completed
judgment” and from which appeal is “independent of the ap-
peal of the original petition”). When properly understood,
then, our decision in Banister actually supports the rule that
Rivers resists.
 2
 Rivers also maintains that it undermines the purposes of
AEDPA, and diverges from historical habeas doctrine and
practice, to conclude that second-in-time applications fled
during the pendency of an appeal trigger § 2244(b). See id.,
at 512–513 (explaining that these factors are relevant to the
second-or-successive inquiry). But purpose and history do
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 Opinion of the Court

not push us in the direction of adopting Rivers's preferred
interpretation either.
 As we have said before, “[t]he point of § 2244(b)'s [gate-
keeping] restrictions . . . is to conserve judicial resources,
reduce piecemeal litigation, and lend fnality to state court
judgments within a reasonable time.” Id., at 512 (internal
quotation marks and alterations omitted). Rivers argues
that his interpretation advances these aims by, for example,
steering new claims to district courts, which have the “tools
and experience that appellate courts lack” to terminate suits
and thereby “haste[n] fnality.” Brief for Petitioner 34 (capi-
talization and boldface deleted). But the reality is quite the
opposite. If the second-or-successive line is drawn at the
end of the appellate-review period, a petitioner could fle any
number of new applications raising new claims during the
pendency of appeal or certiorari review, thereby prolonging
the case seemingly indefnitely. So, as a practical matter
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and in the mine-run case, Rivers's theory would promote in-
effciency by encouraging piecemeal litigation, and would
thus make it substantially more diffcult to “produce a single
fnal judgment for appeal.” Banister, 590 U. S., at 516 .
 Rivers tries to bolster his congressional-intent-related ar-
guments by pointing to other postconviction provisions that
pin “fnality” to the end of appellate review, not to the entry
of judgment. See, e.g., § 2244(d)(1)(A) (running the 1-year
deadline to fle a § 2254 petition from “the date on which the
judgment became fnal by the conclusion of direct review or
the expiration of the time for seeking such review”). We
note, however, that these provisions are buoyed by different
animating purposes. The 1-year deadline for fling a § 2254
petition, for example, promotes exhaustion of claims and re-
spects state-court processes, whereas AEDPA's second-or-
successive restrictions “constitute a modifed res judicata
rule,” Felker v. Turpin, 518 U. S. 651, 664 (1996), that “bal-
ance[s] . . . fnality and error correction,” Jones v. Hendrix,
 599 U. S. 465, 491 (2023). “It is thus hardly `strange' that
456 RIVERS v. GUERRERO

 Opinion of the Court

rules governing exhaustion and the statute of limitations for
purposes of bringing an initial application differ from those
governing a successive application.” Brief for Respondent
38. With AEDPA's second-or-successive bar, Congress
chose to promote fnality by requiring authorization from the
court of appeals to fle successive petitions; the question be-
fore us today is merely when that requirement kicks in.
 Rivers's appeal to historical habeas doctrine fares no bet-
ter because, prior to AEDPA, there was no clear or consist-
ent practice regarding how new habeas-related flings were
treated during the pendency of an appeal. Some courts
would consider new habeas flings on the merits, and deny
them, when the frst-in-time habeas petition was under ap-
pellate review.3 But others would dismiss such flings with-
out reaching the merits, on the ground that they were second
or successive petitions not subject to review.4 It is diffcult
to know what to make of these inconsistent practices, espe-
Page Proof Pending Publication
cially when Rivers fails to point to any case in which a court
actually granted habeas relief on a subsequent petition while
the frst was on appeal. The historical picture is thus far
too murky to be dispositive. Cf. Banister, 590 U. S., at 514–
515 (relying on historical case law that indicated an over-
whelming consensus in favor of the petitioner's view). As
such, Rivers's history and policy arguments do not move the
needle in our analysis.
 In short, we reject Rivers's focus on the timing of his suc-
cessive fling relative to the pendency of his appeal, and we
conclude instead that it is the fnal judgment related to the

 3
 See, e. g., Giarratano v. Procunier, 891 F. 2d 483 , 485–487 (CA4 1989)
(affrming the denial of a mid-appeal Rule 60(b) motion on the merits);
Schewchun v. Edwards, 1987 WL 36402 , *1–*2 (CA6, Feb. 19, 1987) (same).
 4
 See, e. g., Behringer v. Johnson, 75 F. 3d 189 , 189–190 (CA5 1996)
(per curiam) (affrming denial of a Rule 60(b) motion containing new
claims fled while the frst petition was pending on appeal as a successive
habeas petition); Hunt v. Nuth, 57 F. 3d 1327, 1331 , 1338–1339 (CA4
1995) (same).
 Cite as: 605 U. S. 443 (2025) 457

 Opinion of the Court

initial habeas fling that matters. Once the judgment has
been entered with respect to the initial habeas petition, a
second-in-time fling that makes new habeas claims generally
qualifes as a second or successive petition for § 2244(b)
purposes.5
 IV
 Rivers's petition for certiorari posited the question we've
answered above. See Pet. for Cert. 1 (asking “whether 28
U. S. C. § 2244 (b)(2)'s rules for `second or successive' habeas
petitions apply to a habeas fling made after the district
court has denied an initial petition but before an appellate
court has weighed in”).6 But Rivers's merits briefng pivots
to articulate an additional theory, in the alternative: that
second-in-time flings that request amendment of the initial
habeas petition under Rule 15 of the Federal Rules of Civil
Procedure do not—by their nature—qualify as second or suc-
cessive flings under § 2244(b). See Brief for Petitioner 23
Page Proof Pending Publication
(“[A]n `amendment' is not a new and independent application,
but rather something that happens to an existing applica-
tion”); see also id., at 31 (describing Rule 15 motions as “part
and parcel of the initial application” (boldface deleted)). We
decline to address this argument today for two reasons.
 First, Rivers failed to present this argument in his petition
for certiorari or to the courts below. This new theory for
 5
 Although we hold today that an application is second or successive
under § 2244(b) if a judgment on the merits has issued as to a frst-in-time
petition even if the case remains pending on appeal, we neither decide nor
comment on whether the classifcation of a second-in-time petition must
occur while the appeal is pending. That is, we take no position on
whether, in a case where the facts support doing so, a subsequent fling
can be held in abeyance until the frst-in-time appeal has concluded, as is
the common practice in some Circuits. See, e.g., Santarelli, 929 F. 3d, at
105–106.
 6
 See also Pet. for Cert. 2 (claiming that “[t]he Fifth Circuit's decision
deepen[ed] a circuit confict over when § 2244(b)(2) kicks in”); id., at 24
(“Section 2244(b)(2) does not apply until appellate review of the frst ha-
beas application is exhausted” (boldface deleted)).
458 RIVERS v. GUERRERO

 Opinion of the Court

why his successive fling does not trigger § 2244(b) does not
operate on the timing of the fling (i.e., whether, when an
appeal is pending, the fling is “second or successive”), but,
rather, on its nature (i.e., whether, when submitted under
Rule 15, the fling counts as an “application” at all). Rivers
did not cite § 2242—the source of authority upon which he
relies for this alternative argument—until his opening mer-
its brief in this Court. We have often said that “ `[w]e are a
Court of review, not of frst view.' ” Moody v. NetChoice,
LLC, 603 U. S. 707, 726 (2024) (quoting Cutter v. Wilkinson,
 544 U. S. 709, 718, n. 7 (2005)). Rivers's alternative argu-
ment thus “suffers from the legally fatal problem that it
makes its frst appearance here in this Court in the briefs on
the merits.” Ohio Forestry Assn., Inc. v. Sierra Club, 523
U. S. 726, 738 (1998).
 Second, and in any event, we note that the factual predi-
cate necessary for Rivers's Rule 15 argument to help him
Page Proof Pending Publication
in this case is lacking. The District Court could not have
granted Rivers's Rule 15 motion to amend (assuming, ar-
guendo, that we treat his second-in-time fling as such)
while his habeas claims were being considered on appeal,
since jurisdiction had shifted to the Court of Appeals. See
Coinbase, Inc. v. Bielski, 599 U. S. 736, 740 (2023). Recog-
nizing this, Rivers asserts that the District Court could have
issued an indicative ruling on this motion under Rule 62.1,
which, in turn, might have persuaded the Fifth Circuit to
remand the case to the District Court for consideration of
the amendment. But there is one more missing piece (and
it is crucial): Rivers never asked the District Court in this
case for such an indicative ruling. Nor does he argue that
the District Court abused its discretion by failing to issue
one sua sponte. Meanwhile, the Fifth Circuit considered—
and denied—the actual remand motion that Rivers fled with
that court; he asked the Circuit to send the matter back to
the District Court for consideration of the newly discovered
 Cite as: 605 U. S. 443 (2025) 459

 Opinion of the Court

evidence, and we now lack jurisdiction to review its refusal
to do so.7
 Thus, even if Rivers's fling in the District Court could
have been construed as a Rule 15 motion to amend, the Dis-
trict Court was powerless to grant it while his case was on
appeal, and the Fifth Circuit had no proclivity to remand the
matter to the District Court in any event. This means that
Rivers's alternative theory is of no use to him, and, as such,
we decline to address it.

 * * *
 A second-in-time § 2254 petition generally qualifes as a
second or successive application, triggering the require-
ments of § 2244(b), when an earlier fled petition has been
decided on the merits and a judgment exists. Because the
Fifth Circuit correctly applied this straightforward rule, we
affrm.
 It is so ordered.
Page Proof Pending Publication

 7
 That Fifth Circuit ruling was associated with Rivers's frst habeas peti-
tion and is memorialized in a separate docket than the case which is now
on appeal. See App. 9–12. We denied certiorari on April 3, 2023. See
Rivers v. Lumpkin, 598 U. S. 1234 .
 Reporter’s Note

 The attached opinion has been revised to refect the usual publication
and citation style of the United States Reports. The revised pagination
makes available the offcial United States Reports citation in advance of
publication. The syllabus has been prepared by the Reporter of Decisions
Page Proof Pending Publication
for the convenience of the reader and constitutes no part of the opinion of
the Court. A list of counsel who argued or fled briefs in this case, and
who were members of the bar of this Court at the time this case was
argued, has been inserted following the syllabus. Other revisions may
include adjustments to formatting, captions, citation form, and any errant
punctuation. The following additional edits were made:

p. 453, line 16 from bottom: “the” is changed to “a”

PRELIMINARY PRINT Volume 605 U. S. Part 2 Pages 443–459 OFFICIAL REPORTS OF THE SUPREME COURT June 12, 2025 Page Proof Pending Publication REBECCA A. WOMELDORF reporter of decisions NOTICE: This preliminary print is subject to formal revision before the bound volume is published. Users are requested to notify the Reporter of Decisions, Supreme Court of the United States, Washington, D. C. 20543, pio@supremecourt.gov, of any typographical or other formal errors. OCTOBER TERM, 2024 443 Syllabus RIVERS v. GUERRERO, DIRECTOR, TEXAS DE- PARTMENT OF CRIMINAL JUSTICE, COR- RECTIONAL INSTITUTIONS DIVISION certiorari to the united states court of appeals for the fth circuit No. 23–1345. Argued March 31, 2025—Decided June 12, 2025 Petitioner Danny Rivers was convicted in Texas state court of continuous sexual abuse of a child and related charges. After unsuccessfully seek- ing direct appeal and state habeas relief, Rivers fled his frst federal habeas petition under 28 U. S. C. § 2254 in August 2017, asserting claims of prosecutorial misconduct, ineffective assistance of counsel, and other constitutional violations. The District Court denied the petition in Sep- tember 2018, and Rivers appealed to the Fifth Circuit, which granted a certifcate of appealability on his ineffective-assistance claim in July 2020. While his appeal was pending, Rivers obtained his trial counsel's cli- ent fle, which contained a state investigator's report that he believed Page Proof Pending Publication was exculpatory. After the Fifth Circuit denied his request to supple- ment the record on appeal, Rivers fled a second § 2254 petition in the District Court based on this newly discovered evidence. The District Court classifed this second-in-time fling as a “second or successive” habeas application under § 2244(b) and transferred it to the Fifth Circuit for authorization to fle. Rivers appealed the transfer order, and the Fifth Circuit affrmed, holding that the fact that Rivers's frst petition was still on appeal did not permit him to circumvent the requirements for successive petitions under § 2244 as to his second fling. Held: Once a district court enters its judgment with respect to a frst-fled habeas petition, a second-in-time fling qualifes as a “second or succes- sive application” properly subject to the requirements of § 2244(b). Pp. 450–459. (a) The Antiterrorism and Effective Death Penalty Act of 1996 (AEDPA) contains several signifcant procedural barriers that strictly limit a court's ability to hear “claim[s] presented” in any “second or successive habeas corpus application.” §§ 2244(b)(1), (2). Relevant here, § 2244 prohibits habeas applicants from fling a subsequent petition that relitigates the merits of previously denied claims. See § 2244(b)(1). Even if the subsequent petition presents a new claim, the second-in-time application can only proceed if it “relies on a new and retroactive rule of constitutional law” or “alleges previously undis- 444 RIVERS v. GUERRERO Syllabus coverable facts that would establish [the petitioner's] innocence.” Ban- ister v. Davis, 590 U. S. 504, 509 . In addition, a petitioner cannot bring a second or successive habeas application directly to the district court but must frst go to the court of appeals and make a “prima facie showing” that the petition satisfes one of § 2244(b)(2)'s exceptions. Pp. 450–451. (b) The Court has jurisdiction to review this dispute. Respondent contends that Rivers lacks standing because the Fifth Circuit has now affrmed the District Court's judgment denying the initial habeas peti- tion on the merits. But because a favorable decision here would re- dress Rivers's alleged injury that the District Court inappropriately transferred his second habeas application to the Fifth Circuit for review under § 2244(b), Rivers has appellate standing with respect to that legal claim. Nor does the fact that Rivers is no longer in custody on the child-pornography conviction that his second habeas fling challenges defeat this Court's habeas jurisdiction, given that Rivers remains incar- cerated on related sexual-abuse sentences that the newly discovered evidence may implicate. Pp. 451–452. (c) The phrase “second or successive habeas corpus application” in § 2244(b)(2) is a “term of art” that does not refer to all habeas flings made second in time following an initial application. Whether a fling qualifes Page Proof Pending Publication as a second or successive application generally turns on the existence of a fnal judgment with respect to the frst petition, not the status of any appeal. An amended petition fled before judgment is not second or successive because fnal judgment has not issued, while a motion under Federal Rule of Civil Procedure 60(b) fled after judgment counts as a second or successive application if it attacks the court's previous resolu- tion of a claim on the merits or seeks to add new grounds for relief. Rivers's argument that his second fling should not trigger § 2244(b) because his appeal was pending is unpersuasive. The Court's decision in Banister v. Davis, 590 U. S. 504 , does not support a rule that is based on appeal timing but rather confrms that entry of fnal judgment gener- ally separates frst from second or successive habeas flings. Rule 59(e) motions present a unique variant because they suspend fnality and help produce a single fnal judgment, but Rivers's fling does not fall within this narrow category. Pp. 452–454. (d) Purpose and history do not support Rivers's interpretation either. Section 2244(b)'s restrictions aim to conserve judicial resources, reduce piecemeal litigation, and lend fnality to state-court judgments within a reasonable time. Drawing the second-or-successive line at the end of appellate review would allow petitioners to fle numerous new applica- tions during appeals, prolonging cases and encouraging piecemeal litiga- tion. Historical habeas doctrine before AEDPA was inconsistent re- Cite as: 605 U. S. 443 (2025) 445 Syllabus garding treatment of new flings during pending appeals, providing no clear guidance. Pp. 454–457. (e) The Court declines to address Rivers's alternative argument that his second fling, which he argues was a Rule 15 motion to amend, is not a new application by its nature. This theory was not presented in the petition for certiorari or to the courts below and makes its frst appear- ance in the merits briefng. Additionally, the factual predicate is lack- ing because the District Court lacked jurisdiction to grant such a motion while the case was on appeal, and Rivers never requested an indicative ruling under Rule 62.1. Pp. 457–459. 99 F. 4th 216 , affrmed. Jackson, J., delivered the opinion for a unanimous Court. Peter A. Bruland argued the cause for petitioner. With him on the briefs were Virginia A. Seitz, Benjamin M. Mun- del, Cody M. Akins, and Jacob Steinberg-Otter. Aaron L. Nielson, Solicitor General of Texas, argued the cause for respondent. With him on the brief were Ken Pax- ton, Attorney General, Brent Webster, First Assistant Attor- Page Proof Pending Publication ney General, William F. Cole, Principal Deputy Solicitor General, Jacob C. Beach, Assistant Solicitor General, Joseph P. Corcoran, Deputy Chief, Criminal Appeals Division, and Lori Brodbeck, Meagan Corser, and Justine Tan, Assistant Attorneys General. Matthew Guarnier i argued the cause for the United States as amicus curiae urging affrmance. With him on the brief were Acting Solicitor General Harris, Deputy So- licitor General Feigin, and Antoinette T. Bacon.* *Briefs of amici curiae urging reversal were fled for Former Federal and State Prosecutors by Joshua D. Branson and Jarrod A. Nagurka; for Former Federal Judges by Andrew T. Tutt and Dana Kagan McGinley; for the National Association of Federal Defenders et al. by Jonathan Kirsh- baum, Shelley Fite, David M. Porter, Rachel Julagay, and David F. Ness; and for Phillips Black, Inc., by John R. Mills. Briefs of amici curiae urging affrmance were fled for the State of Arkansas et al. by Tim Griffn, Attorney General of Arkansas, Dylan L. Jacobs, Interim Solicitor General, and Asher L. Steinberg, Senior Assistant Solicitor General, by Christopher M. Carr, Attorney General of Georgia, 446 RIVERS v. GUERRERO Opinion of the Court Justice Jackson delivered the opinion of the Court. Incarcerated individuals who seek to challenge their im- prisonment through a federal habeas petition are generally afforded one opportunity to do so. See 28 U. S. C. §§ 2254 , 2244. Before a federal court can address a petitioner's sec- ond or successive federal habeas fling on the merits, the incarcerated fler must clear strict procedural hurdles that the Antiterrorism and Effective Death Penalty Act of 1996 (AEDPA) erects. See § 2244(b). This case pre- sents the question of how to classify a second-in-time habeas fling when the judgment denying the frst application is under review on appeal. Does that second habeas-related submission qualify as a second or successive application, thereby triggering § 2244(b)'s stringent gatekeeping requirements? We hold that, in general, once the district court has en- tered its judgment with respect to the frst habeas petition, Page Proof Pending Publication a second-in-time application qualifes as “second or succes- Stephen J. Petrany, Solicitor General, and Justin T. Golart, Deputy Solici- tor General, and by the Attorneys General for their respective States as follows: Steve Marshall of Alabama, James Uthmeier of Florida, Raúl Labrador of Idaho, Theodore E. Rokita of Indiana, Brenna Bird of Iowa, Kris W. Kobach of Kansas, Russell Coleman of Kentucky, Liz Murrill of Louisiana, Lynn Fitch of Mississippi, Andrew Bailey of Missouri, Michael T. Hilgers of Nebraska, Aaron D. Ford of Nevada, Drew H. Wrigley of North Dakota, Dave Yost of Ohio, Gentner Drummond of Oklahoma, Alan Wilson of South Carolina, Marty J. Jackley of South Dakota, Jonathan Skrmetti of Tennessee, Derek Brown of Utah, Jason Miyares of Virginia, and Patrick Morrisey of West Virginia; for the Commonwealth of Pennsyl- vania et al. by David W. Sunday, Jr., Attorney General of Pennsylvania, Hugh J. Burns, Jr., and Ronald Eisenberg, Senior Deputy Attorneys Gen- eral, Kirsten E. Heine, Executive Deputy Attorney General, Kathleen Jen- nings, Attorney General of Delaware, and Matthew J. Platkin, Attorney General of New Jersey; for the Criminal Justice Legal Foundation by Kent S. Scheidegger; and for Sen. John Cornyn by Owen J. McGovern. Igor V. Timofeyev, Stephen B. Kinnaird, Vladimir J. Semendyai, and Vanessa Omoroghomwan fled a brief for Lee Kovarsky et al. as amici curiae. Cite as: 605 U. S. 443 (2025) 447 Opinion of the Court sive” and is thus properly subject to the requirements of § 2244(b). I In 2012, a Texas state-court jury convicted petitioner Danny Rivers of continuous sexual abuse of a child, two forms of indecency with a child, and possession of child por- nography. Rivers unsuccessfully sought direct appeal and state habeas relief. In August 2017, Rivers fled his frst federal habeas peti- tion under 28 U. S. C. § 2254 , a statute that permits a federal court to evaluate a state prisoner's claim “that he is in cus- tody in violation of the Constitution or laws or treaties of the United States.” § 2254(a). In that habeas petition, Rivers asserted, inter alia, claims of prosecutorial misconduct, inef- fective assistance of trial and appellate counsel, and due process and equal protection violations. The District Court denied Rivers's habeas petition, issuing Page Proof Pending Publication its judgment in September 2018. Rivers then invoked the procedure that AEDPA prescribes for seeking to challenge a § 2254 habeas denial in the court of appeals: He asked the Fifth Circuit to give him what is known as a “certifcate of appealability.” 1 A Fifth Circuit Judge granted Rivers's re- quest in July 2020, but only as to his claim for ineffective assistance of counsel. While his appeal was pending, Rivers gained access to his own client fle, which had been in his trial counsel's posses- sion. The fle contained a state investigator's report that discussed two computer documents Rivers believed were re- 1 Individuals seeking to appeal the denial of a § 2254 habeas petition must receive permission to do so by obtaining such a certifcate. See § 2253(c)(1)(A) (“[A]n appeal may not be taken to the court of appeals from . . . the fnal order in a habeas corpus proceeding in which the detention complained of arises out of process issued by a State court” “[u]nless a circuit justice or judge issues a certifcate of appealability”). A certifcate of appealability can issue “only if the applicant has made a substantial showing of the denial of a constitutional right.” § 2253(c)(2). 448 RIVERS v. GUERRERO Opinion of the Court lated to his convictions; one document was labeled “of inter- est,” while the other was specifcally described as “not child porn.” App. 94 (capitalization deleted). Rivers promptly requested to supplement the Fifth Circuit's case record with this purportedly exculpatory information, but the Fifth Cir- cuit denied that request. Rivers then asked the appellate panel to either stay the appeal or remand the case to the District Court to allow him to present this new evidence to the lower court in the frst instance. See id., at 99 (arguing that “justice and judicial economy would best be served” if a single court considered “all grounds” for relief (capitalization deleted)). The Fifth Circuit rejected the stay-or-remand request as well and, thereafter, affrmed the District Court's denial of Rivers's § 2254 petition on the merits. This Court denied certiorari. See Rivers v. Lumpkin, 598 U. S. 1234 (2023). Notably for present purposes, after the Fifth Circuit de- Page Proof Pending Publication nied Rivers's request to supplement the record, Rivers fled another § 2254 petition with the District Court. This peti- tion included the newly obtained state investigator's report and raised claims for relief related to that evidence. A Mag- istrate Judge recommended that this second-in-time habeas petition be classifed as a “second or successive” habeas ap- plication for § 2244(b) purposes. Rivers objected, arguing that his second § 2254 fling should not be construed as a new habeas application. Rather, Rivers asserted, the new fling should be treated as an amendment to his initial habeas peti- tion, because the judgment related to that frst petition was still on appeal. The District Court rejected Rivers's argument. It con- cluded that the second-in-time fling was a second or succes- sive habeas petition subject to § 2244(b)(2) and transferred the fling to the Fifth Circuit for a determination whether § 2244(b)(2)'s gatekeeping requirements for second or succes- sive habeas petitions had been satisfed. See Part II, infra. Rivers then appealed the District Court's transfer order, Cite as: 605 U. S. 443 (2025) 449 Opinion of the Court again insisting that his fling was not a second or successive habeas petition (as opposed to a motion to amend) “because his frst-in-time petition was still pending on appeal.” Riv- ers v. Lumpkin, 99 F. 4th 216, 218 (CA5 2024). The Fifth Circuit affrmed. In its view, “the timing of Rivers's second-in-time petition d[id] not permit him to cir- cumvent the requirements for fling successive petitions under § 2244.” Id., at 221. The panel reasoned that the District Court could have treated the second-in-time fling as a request to amend under Federal Rule of Civil Procedure 15 if the judgment relating to Rivers's frst petition had been vacated on appeal and the case reopened in the District Court. Ibid. But because the judgment as to the frst peti- tion had not been so vacated, “Rivers's second-in-time habeas petition” was a “second or successive” petition that was “sub- ject to the district court's transfer order for lack of jurisdic- tion absent authorization to fle.” Id., at 223. Page Proof Pending Publication The Fifth Circuit's decision entrenched a Circuit split over how to characterize a second-in-time habeas fling that is fled when an appeal of the judgment of the frst habeas fling is pending.2 Is the second fling a “second or successive” habeas petition for § 2244 purposes, or not? We granted cer- tiorari to resolve that split. 604 U. S. 1041 (2024). 2 The majority of Circuits to consider the issue have concluded that § 2244(b) applies to a second-in-time habeas fling as of the district court's entry of fnal judgment related to the frst application, regardless of the status of any appeal. See, e. g., Balbuena v. Sullivan, 980 F. 3d 619 , 641– 642 (CA9 2020); Phillips v. United States, 668 F. 3d 433 , 435–436 (CA7 2012); Ochoa v. Sirmons, 485 F. 3d 538 , 540–541 (CA10 2007) (per curiam); Williams v. Norris, 461 F. 3d 999 , 1003–1004 (CA8 2006). The Second Circuit, by contrast, has held that “so long as appellate proceedings follow- ing the district court's dismissal of the initial petition remain pending when a subsequent petition is fled, the subsequent petition does not come within AEDPA's gatekeeping provisions for `second or successive' peti- tions.” Whab v. United States, 408 F. 3d 116, 118 (2005) (emphasis added); see also United States v. Santarelli, 929 F. 3d 95, 105 (CA3 2019) (“join- [ing] the Second Circuit”). 450 RIVERS v. GUERRERO Opinion of the Court II Habeas petitioners are generally entitled to “one fair op- portunity” to litigate the merits of their postconviction claims in federal court. Banister v. Davis, 590 U. S. 504, 507 (2020); see also Slack v. McDaniel, 529 U. S. 473 , 485–486 (2000); Stewart v. Martinez-Villareal, 523 U. S. 637, 643 (1998). When a person seeks to bring a subsequent federal habeas challenge to his detention, “the road gets rockier.” Banister, 590 U. S., at 509 . AEDPA contains several sig- nifcant procedural barriers that strictly limit a court's abil- ity to hear “claim[s] presented” in any “second or successive habeas corpus application.” §§ 2244(b)(1), (2). Several of those barriers are relevant to the issue pre- sented in this case. First, § 2244 prohibits habeas applicants from fling a subsequent petition that relitigates the merits of previously denied claims. See § 2244(b)(1) (stating that any claim that “was presented in a prior application shall be Page Proof Pending Publication dismissed”). Second, even if the subsequent petition pre- sents a new claim, the second-in-time application can only proceed if it “falls within one of two narrow categories”: The claim must “rel[y] on a new and retroactive rule of constitu- tional law” or “alleg[e] previously undiscoverable facts that would establish [the petitioner's] innocence.” Banister, 590 U. S., at 509 ; see also § 2244(b)(2). Additionally, a petitioner cannot bring a second or successive habeas application di- rectly to the district court. Instead, he must frst go to the court of appeals and make a “prima facie showing” that the petition satisfes one of § 2244(b)(2)'s exceptions, and that court has to grant authorization for the petitioner to proceed in district court. § 2244(b)(3). And then, even when such leave is granted, the district court must independently con- firm that the petition satisfies the requirements of § 2244(b)(2). See § 2244(b)(4). These rules apply to second-in-time habeas flings even if the fling is not styled as a § 2254 habeas application by the Cite as: 605 U. S. 443 (2025) 451 Opinion of the Court fler—so long as the document is a § 2254 petition in sub- stance. For example, a self-styled “motion” that “seeks to add a new ground for relief ” or “attacks the federal court's previous resolution of a claim on the merits” can be con- strued as a second or successive petition and forced to face the gauntlet of § 2244(b), no matter how it is labeled. Gon- zalez v. Crosby, 545 U. S. 524, 532 (2005) (emphasis deleted). III Respondent presents two arguments for why we lack ju- risdiction over today's dispute about how Rivers's second-in- time habeas fling should be characterized: frst, that Rivers lacks standing because his injury is not redressable; and sec- ond, that the Court lacks habeas jurisdiction because Riv- ers's child-pornography sentence has expired. For his part, Rivers makes two alternative arguments about the merits. He maintains that the second-in-time habeas petition does not trigger the second-or-successive requirements of Page Proof Pending Publication § 2244(b) because his appeal of the frst petition was pending when he fled the second one. Alternatively, he argues that his second-in-time fling should be construed as a motion to amend—and, so construed, does not qualify as an “applica- tion” to which § 2244(b)'s requirements apply. A We begin our analysis by quickly disposing of respondent's contention that we lack jurisdiction. Respondent frst in- sists that Rivers lacks standing because the Fifth Circuit has now affrmed the District Court's judgment denying the ini- tial habeas petition on the merits, and this Court lacks the authority to reopen that judgment in this separate litigation. But a favorable decision from this Court would redress Riv- ers's alleged injury—namely, that the District Court inap- propriately transferred his second-in-time habeas application to the Fifth Circuit for review under § 2244(b). Rivers 452 RIVERS v. GUERRERO Opinion of the Court therefore has appellate standing with respect to that legal claim. See Food Marketing Institute v. Argus Leader Media, 588 U. S. 427, 433 (2019). Respondent is also mistaken regarding the contention that the Court lacks habeas jurisdiction because Rivers is no longer in custody on the child-pornography conviction that the second habeas fling challenges. See § 2254(a) (permit- ting an application from an individual “in custody”). The record establishes that the newly discovered evidence Rivers wants the federal courts to consider implicates the sexual- abuse sentences for which Rivers remains incarcerated, too. Thus, we retain habeas jurisdiction to review his claims. B 1 Turning to the parties' merits arguments concerning Riv- ers's second-in-time habeas fling, we note, to start, that the Page Proof Pending Publication phrase “second or successive . . . application” as it appears in § 2244(b)(2) is a “term of art”—that is, it does not necessarily “ `refer' to all habeas flings made `second or successively in time,' following an initial application.” Banister, 590 U. S., at 511 (quoting Magwood v. Patterson, 561 U. S. 320, 332 (2010)). Instead, the second-or-successive moniker applies only to “claim[s]” that have been presented in subsequently fled “applications.” § 2244(b)(2). A “claim,” as that term is used in § 2244(b), is “an asserted federal basis for relief ” from the judgment of conviction. Gonzalez, 545 U. S., at 530 . And an “application” is “a fling that seeks `an adjudi- cation' ” of one of those claims “ `on the merits.' ” Ibid. (quoting Woodford v. Garceau, 538 U. S. 202, 207 (2003); em- phasis deleted); see also Gonzalez, 545 U. S., at 533 (explain- ing that motions that do not “substantively addres[s] federal grounds for setting aside the movant's state conviction,” for example, are not subject to the second-or-successive bar). Rivers acknowledges that his second-in-time fling “raised several new claims” that he had not presented previously to Cite as: 605 U. S. 443 (2025) 453 Opinion of the Court the District Court. Pet. for Cert. 12. Still, in his petition for certiorari—and, to a lesser extent, his merits brief—Riv- ers argues that this fling did not qualify as a second or suc- cessive application triggering § 2244(b) because it was sub- mitted during the pendency of his appeal of the judgment related to his frst habeas petition. Id., at 24; Brief for Peti- tioner 37. We do not agree with that proposition. Our case law establishes instead that whether a fling qualifes as a second or successive application generally turns on the exist- ence of a fnal judgment with respect to the frst petition, not the status of an appeal. We have noted, for example, that “an amended petition, fled after the initial one but before judgment, is not second or successive” for § 2244(b) purposes precisely because fnal judgment has not issued. Banister, 590 U. S., at 512 (em- phasis added). On the other hand, we have determined that a motion for relief from judgment under Federal Rule of Page Proof Pending Publication Civil Procedure 60(b) (fled, obviously, after the judgment has issued) counts as a second or successive application if that fling “attacks the federal court's previous resolution of a claim on the merits” or “seeks to add a new ground for relief ” not addressed by the judgment. Gonzalez, 545 U. S., at 532 (emphasis deleted). Pointing to Banister, Rivers insists that this Court has already rejected a moment-of-judgment rule for distinguish- ing between second-in-time flings that qualify as second or successive applications and those that do not. But our rul- ing in Banister related to a materially different fling sub- mitted in a materially different context. There, the Court considered whether a motion to alter or amend a judgment under Federal Rule of Civil Procedure 59(e)—i.e., a motion fled within 28 days that seeks to correct an error in the District Court's judgment prior to an appeal—should be con- strued as a second or successive fling under § 2244(b). 590 U. S., at 511 . To be sure, the respondent in that case had “urged this Court to hold that `[e]ntry of fnal judgment is 454 RIVERS v. GUERRERO Opinion of the Court the dividing line between a frst and second application,' ” as Rivers notes. Brief for Petitioner 37 (quoting Brief for Respondent in Banister v. Davis, O. T. 2019, No. 18–6943, p. 18; alteration in original). But Rule 59(e) motions present a unique variant to the otherwise generally applicable rule that entry of fnal judgment separates frst from second or successive habeas flings. Specifcally, unlike a Rule 60(b) motion for relief from judg- ment, which seeks to challenge an extant judgment, a suc- cessful Rule 59(e) motion merely “suspends fnality” of the original judgment so that the district court can “fx any mis- takes and thereby perfect its judgment before a possible ap- peal.” Banister, 590 U. S., at 516 . A Rule 59(e) motion is “a limited continuation of the original proceeding—indeed, a part of producing the fnal judgment granting or denying habeas relief.” Id., at 521 . As a result, disposition on a Rule 59(e) motion “merges into the fnal judgment” of the initial habeas fling. Id., at 516 . Page Proof Pending Publication In other words, Rule 59(e) motions are “attendant on the initial habeas application” itself and “hel[p] produce a single fnal judgment for appeal.” Id., at 515–516. Thus, they are not themselves properly considered to be second or suc- cessive flings under AEDPA. Id., at 517 ; see also id., at 518–520 (contrasting this with second-in-time flings that “collaterally attack [the District Court's] already completed judgment” and from which appeal is “independent of the ap- peal of the original petition”). When properly understood, then, our decision in Banister actually supports the rule that Rivers resists. 2 Rivers also maintains that it undermines the purposes of AEDPA, and diverges from historical habeas doctrine and practice, to conclude that second-in-time applications fled during the pendency of an appeal trigger § 2244(b). See id., at 512–513 (explaining that these factors are relevant to the second-or-successive inquiry). But purpose and history do Cite as: 605 U. S. 443 (2025) 455 Opinion of the Court not push us in the direction of adopting Rivers's preferred interpretation either. As we have said before, “[t]he point of § 2244(b)'s [gate- keeping] restrictions . . . is to conserve judicial resources, reduce piecemeal litigation, and lend fnality to state court judgments within a reasonable time.” Id., at 512 (internal quotation marks and alterations omitted). Rivers argues that his interpretation advances these aims by, for example, steering new claims to district courts, which have the “tools and experience that appellate courts lack” to terminate suits and thereby “haste[n] fnality.” Brief for Petitioner 34 (capi- talization and boldface deleted). But the reality is quite the opposite. If the second-or-successive line is drawn at the end of the appellate-review period, a petitioner could fle any number of new applications raising new claims during the pendency of appeal or certiorari review, thereby prolonging the case seemingly indefnitely. So, as a practical matter Page Proof Pending Publication and in the mine-run case, Rivers's theory would promote in- effciency by encouraging piecemeal litigation, and would thus make it substantially more diffcult to “produce a single fnal judgment for appeal.” Banister, 590 U. S., at 516 . Rivers tries to bolster his congressional-intent-related ar- guments by pointing to other postconviction provisions that pin “fnality” to the end of appellate review, not to the entry of judgment. See, e.g., § 2244(d)(1)(A) (running the 1-year deadline to fle a § 2254 petition from “the date on which the judgment became fnal by the conclusion of direct review or the expiration of the time for seeking such review”). We note, however, that these provisions are buoyed by different animating purposes. The 1-year deadline for fling a § 2254 petition, for example, promotes exhaustion of claims and re- spects state-court processes, whereas AEDPA's second-or- successive restrictions “constitute a modifed res judicata rule,” Felker v. Turpin, 518 U. S. 651, 664 (1996), that “bal- ance[s] . . . fnality and error correction,” Jones v. Hendrix, 599 U. S. 465, 491 (2023). “It is thus hardly `strange' that 456 RIVERS v. GUERRERO Opinion of the Court rules governing exhaustion and the statute of limitations for purposes of bringing an initial application differ from those governing a successive application.” Brief for Respondent 38. With AEDPA's second-or-successive bar, Congress chose to promote fnality by requiring authorization from the court of appeals to fle successive petitions; the question be- fore us today is merely when that requirement kicks in. Rivers's appeal to historical habeas doctrine fares no bet- ter because, prior to AEDPA, there was no clear or consist- ent practice regarding how new habeas-related flings were treated during the pendency of an appeal. Some courts would consider new habeas flings on the merits, and deny them, when the frst-in-time habeas petition was under ap- pellate review.3 But others would dismiss such flings with- out reaching the merits, on the ground that they were second or successive petitions not subject to review.4 It is diffcult to know what to make of these inconsistent practices, espe- Page Proof Pending Publication cially when Rivers fails to point to any case in which a court actually granted habeas relief on a subsequent petition while the frst was on appeal. The historical picture is thus far too murky to be dispositive. Cf. Banister, 590 U. S., at 514– 515 (relying on historical case law that indicated an over- whelming consensus in favor of the petitioner's view). As such, Rivers's history and policy arguments do not move the needle in our analysis. In short, we reject Rivers's focus on the timing of his suc- cessive fling relative to the pendency of his appeal, and we conclude instead that it is the fnal judgment related to the 3 See, e. g., Giarratano v. Procunier, 891 F. 2d 483 , 485–487 (CA4 1989) (affrming the denial of a mid-appeal Rule 60(b) motion on the merits); Schewchun v. Edwards, 1987 WL 36402 , *1–*2 (CA6, Feb. 19, 1987) (same). 4 See, e. g., Behringer v. Johnson, 75 F. 3d 189 , 189–190 (CA5 1996) (per curiam) (affrming denial of a Rule 60(b) motion containing new claims fled while the frst petition was pending on appeal as a successive habeas petition); Hunt v. Nuth, 57 F. 3d 1327, 1331 , 1338–1339 (CA4 1995) (same). Cite as: 605 U. S. 443 (2025) 457 Opinion of the Court initial habeas fling that matters. Once the judgment has been entered with respect to the initial habeas petition, a second-in-time fling that makes new habeas claims generally qualifes as a second or successive petition for § 2244(b) purposes.5 IV Rivers's petition for certiorari posited the question we've answered above. See Pet. for Cert. 1 (asking “whether 28 U. S. C. § 2244 (b)(2)'s rules for `second or successive' habeas petitions apply to a habeas fling made after the district court has denied an initial petition but before an appellate court has weighed in”).6 But Rivers's merits briefng pivots to articulate an additional theory, in the alternative: that second-in-time flings that request amendment of the initial habeas petition under Rule 15 of the Federal Rules of Civil Procedure do not—by their nature—qualify as second or suc- cessive flings under § 2244(b). See Brief for Petitioner 23 Page Proof Pending Publication (“[A]n `amendment' is not a new and independent application, but rather something that happens to an existing applica- tion”); see also id., at 31 (describing Rule 15 motions as “part and parcel of the initial application” (boldface deleted)). We decline to address this argument today for two reasons. First, Rivers failed to present this argument in his petition for certiorari or to the courts below. This new theory for 5 Although we hold today that an application is second or successive under § 2244(b) if a judgment on the merits has issued as to a frst-in-time petition even if the case remains pending on appeal, we neither decide nor comment on whether the classifcation of a second-in-time petition must occur while the appeal is pending. That is, we take no position on whether, in a case where the facts support doing so, a subsequent fling can be held in abeyance until the frst-in-time appeal has concluded, as is the common practice in some Circuits. See, e.g., Santarelli, 929 F. 3d, at 105–106. 6 See also Pet. for Cert. 2 (claiming that “[t]he Fifth Circuit's decision deepen[ed] a circuit confict over when § 2244(b)(2) kicks in”); id., at 24 (“Section 2244(b)(2) does not apply until appellate review of the frst ha- beas application is exhausted” (boldface deleted)). 458 RIVERS v. GUERRERO Opinion of the Court why his successive fling does not trigger § 2244(b) does not operate on the timing of the fling (i.e., whether, when an appeal is pending, the fling is “second or successive”), but, rather, on its nature (i.e., whether, when submitted under Rule 15, the fling counts as an “application” at all). Rivers did not cite § 2242—the source of authority upon which he relies for this alternative argument—until his opening mer- its brief in this Court. We have often said that “ `[w]e are a Court of review, not of frst view.' ” Moody v. NetChoice, LLC, 603 U. S. 707, 726 (2024) (quoting Cutter v. Wilkinson, 544 U. S. 709, 718, n. 7 (2005)). Rivers's alternative argu- ment thus “suffers from the legally fatal problem that it makes its frst appearance here in this Court in the briefs on the merits.” Ohio Forestry Assn., Inc. v. Sierra Club, 523 U. S. 726, 738 (1998). Second, and in any event, we note that the factual predi- cate necessary for Rivers's Rule 15 argument to help him Page Proof Pending Publication in this case is lacking. The District Court could not have granted Rivers's Rule 15 motion to amend (assuming, ar- guendo, that we treat his second-in-time fling as such) while his habeas claims were being considered on appeal, since jurisdiction had shifted to the Court of Appeals. See Coinbase, Inc. v. Bielski, 599 U. S. 736, 740 (2023). Recog- nizing this, Rivers asserts that the District Court could have issued an indicative ruling on this motion under Rule 62.1, which, in turn, might have persuaded the Fifth Circuit to remand the case to the District Court for consideration of the amendment. But there is one more missing piece (and it is crucial): Rivers never asked the District Court in this case for such an indicative ruling. Nor does he argue that the District Court abused its discretion by failing to issue one sua sponte. Meanwhile, the Fifth Circuit considered— and denied—the actual remand motion that Rivers fled with that court; he asked the Circuit to send the matter back to the District Court for consideration of the newly discovered Cite as: 605 U. S. 443 (2025) 459 Opinion of the Court evidence, and we now lack jurisdiction to review its refusal to do so.7 Thus, even if Rivers's fling in the District Court could have been construed as a Rule 15 motion to amend, the Dis- trict Court was powerless to grant it while his case was on appeal, and the Fifth Circuit had no proclivity to remand the matter to the District Court in any event. This means that Rivers's alternative theory is of no use to him, and, as such, we decline to address it. * * * A second-in-time § 2254 petition generally qualifes as a second or successive application, triggering the require- ments of § 2244(b), when an earlier fled petition has been decided on the merits and a judgment exists. Because the Fifth Circuit correctly applied this straightforward rule, we affrm. It is so ordered. Page Proof Pending Publication 7 That Fifth Circuit ruling was associated with Rivers's frst habeas peti- tion and is memorialized in a separate docket than the case which is now on appeal. See App. 9–12. We denied certiorari on April 3, 2023. See Rivers v. Lumpkin, 598 U. S. 1234 . Reporter’s Note The attached opinion has been revised to refect the usual publication and citation style of the United States Reports. The revised pagination makes available the offcial United States Reports citation in advance of publication. The syllabus has been prepared by the Reporter of Decisions Page Proof Pending Publication for the convenience of the reader and constitutes no part of the opinion of the Court. A list of counsel who argued or fled briefs in this case, and who were members of the bar of this Court at the time this case was argued, has been inserted following the syllabus. Other revisions may include adjustments to formatting, captions, citation form, and any errant punctuation. The following additional edits were made: p. 453, line 16 from bottom: “the” is changed to “a”

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