PATRICK E. HIGGINBOTHAM, Circuit Judge:
Billy Lampton, a prisoner in the custody of the United States, seeks our authorization under 28 U.S.C. § 2255(h) to file a second or successive petition to vacate, set aside, or correct his sentence in the district court where the sentence was imposed. After determining that Lampton’s petition would in fact be “second or successive” within the meaning of § 2255(h), we deny his motion for authorization to file it.
I.
A jury convicted Lampton of six offenses: three counts of distribution of heroin, one count of fraudulent use of a telecommunications instrument, one count of conspiracy to distribute heroin and marijuana, and one count of engaging in a continuing criminal enterprise. In August of 1997, the Eastern District of Louisiana sentenced Lampton to 360 months imprisonment on each of the distribution-of-heroin convictions, 120 months imprisonment on the telecom-fraud conviction, and life imprisonment on both the conspiracy conviction and the continuing-criminal-enterprise (“CCE”) conviction. The district court’s judgment and probation/eommitment order directed that all of the sentences would run concurrently. A panel of this Court affirmed Lampton’s convictions and sentence on direct appeal.
Lampton later filed his first § 2255 petition. The district court granted the petition in part and denied the petition in part. The district court determined that Lamp-ton’s convictions for both conspiracy and CCE violated the constitutional prohibition against double jeopardy. In March of 2001, the district court entered a judgment vacating Lampton’s conspiracy conviction and the life sentence that had been imposed based on that conviction and denying the balance of Lampton’s claims for relief. Lampton sought to appeal the denial of the rest of his claims, but this Court denied him a certificate of appealability.
Between 2003 and 2010, Lampton filed ten challenges to his convictions and sentence: three motions for authorization to file successive § 2255 petitions, three petitions under 28 U.S.C. § 2241, three motions under Federal Rule of Civil Procedure 60(b), and one motion for a nunc pro tunc order. All ten were dismissed or denied. This steady stream of filings prompted this Court to warn Lampton in 2010 that “filing further frivolous challenges to his conviction and sentence could result in the imposition of sanctions.”
Lampton instituted the current proceedings in the district court by filing a § 2255 petition. Lampton contends that his petition is not second or successive (and thus that he was not required by § 2255(h) to obtain this Court’s authorization before filing it) “because it is his first § 2255 motion challenging his amended judgment of conviction.” Relying on the Supreme Court’s recent decision in Magwood v. Patterson, Lampton argues that because the district court granted his first § 2255 petition in part, he is now in custody pursuant to a new, amended judgment and that he has never filed a § 2255 petition challenging this new, amended judgment. The district court determined that the petition was successive and transferred it to this Court.
II.
We conclude that Lampton’s petition is “second or successive” within the meaning of 28 U.S.C. § 2255(h). Mag-wood holds that when a first habeas petition results in the issuance of a new judgment, a later-in-time petition challenging that new judgment is not a “second or successive petition” under AEDPA. AED-PA uses the phrase “ ‘second or successive’ as a ‘term of art.’ ” The phrase appears in both § 2244 and § 2255, and it carries the same meaning in both provisions. The phrase does not encompass all “applications filed second or successively in time.” Rather, it “must be interpreted with respect to the judgment challenged.” As a consequence, where the granting of an initial habeas petition results in the issuance of a new, intervening judgment of conviction, “an application challenging the resulting new judgment is not ‘second or successive’ ” within the meaning of the statute. AEDPA’s bar on second or successive petitions only applies to a later-in-time petition that challenges the same state-court judgment as an earlier-in-time petition.
Whether a new judgment has intervened between two habeas petitions, such that the second petition can be filed without this Court’s permission, depends on whether a new sentence has been imposed. In Magwood, the granting of the petitioner’s first petition resulted in him being re-sentenced after a second round of state-court sentencing proceedings. In In re Barnes, the petitioner’s first habeas petition was dismissed on limitations grounds. He later filed a motion in state court to correct his life sentence. The motion was granted, and Barnes’s life sentence was “corrected” to be a 99-year sentence. We held that he could file another § 2254 petition without obtaining prior authorization from this Court under § 2244 “[bjecause a new sentence constitutes a new judgment.” By contrast, in In re Martin, the Tenth Circuit held that Magwood did not apply where, after the petitioner’s first § 2254 petition had been denied, the state court had entered an amended judgment that “merely corrected a clerical error” — ■ specifically, a typographical error — in the judgment of conviction. The petitioner’s sentence was undisturbed, so no new judgment had been interposed.
It has long been the law of this Circuit that where a defendant has been improperly convicted of and sentenced on both a greater offense and a lesser-included offense, “the proper remedy is to vacate both the conviction and sentence on the included offense, leaving the conviction and sentence on the greater offense intact.” Thus, when a first habeas petition results in vacatur of the conviction and sentence associated with one count of a multi-count conviction, the district court is not required to enter a new judgment as to the remaining counts. Those convictions and sentences, as well as the judgment imposing them, remain undisturbed.
In this case, we conclude that Lampton’s petition seeks to challenge the same judgment of conviction that was the subject of his first § 2255 petition. Lampton is still serving the same life sentence on the same CCE conviction that was imposed by the judgment entered in August of 1997. Lampton’s prior § 2255 petition did not yield a new judgment of conviction. Federal Rule of Criminal Procedure 32(k)(l) requires “the judgment of conviction” to “set forth the plea, the jury verdict or the court’s findings, the adjudication, and the sentence.” The August 1997 judgment is the only document in the record that satisfies those requirements. The judgment entered by the district court in March of 2001 after disposing of Lampton’s § 2255 motion did not satisfy Rule 32(k)(l). Rather, that judgment served to terminate the § 2255 proceeding, which this Court regards “as being civil in nature.” In both Magwood and Barnes, the prior petition had yielded a new sentence, and hence a new judgment. Not so here; Lampton’s sentence on the CCE conviction remained intact after the initial § 2255 proceeding was completed. Therefore, we conclude that there is no new, intervening judgment to trigger the operation of Magwood and hold that Lampton’s instant petition is “second or successive” within the meaning of § 2255(h).
We note that the Second Circuit has concluded, on virtually identical facts, that when a court enters an amended judgment after vacating one of two concurrent sentences, the amended judgment constitutes a new judgment for purposes of the rule announced in Magwood. In that case, though, the Government conceded that the petition was not successive. In this case, upon a request by this Court for briefing, the Government makes no such concession, instead arguing that Lampton’s petition is successive. More fundamentally, the rule announced in Magwood applies only when a new sentence was imposed as a result of the first habeas proceeding. The district court did not enter an amended judgment of conviction in this case. No new sentence was imposed. The less fundamental change made to Lampton’s judgment of conviction is not enough to allow him to bypass AEDPA’s restrictions on piecemeal habeas litigation.
III.
Having determined that Lampton’s petition is second or successive, we now conclude that Lampton has failed to make a prima facie showing that his petition satisfies the requirements of § 2255(h). As relevant here, § 2255(h) authorizes the filing of a second or successive petition only if the petition relies on “a new rule of constitutional law, made retroactive to cases on collateral review by the Supreme Court, that was previously unavailable.” The two claims in Lampton’s petition do not rely on a such a rule. Lampton first argues that he is entitled to relief under Padilla v. Kentucky, Assuming without deciding that the Court has made Padilla retroactive to cases on collateral review, Padilla — which holds that counsel renders deficient performance by failing to advise a non-citizen defendant of the possible deportation consequences of a guilty plea— provides no succor to Lampton, a citizen who was convicted by a jury. Lampton also points to United States v. O’Brien, but O’Brien is a statutory-interpretation case about the elements of an offense under 18 U.S.C. § 924(c)(l)(B)(ii). Section 2255 authorizes a successive filing only when the Supreme Court announces a new rule of constitutional law.
Lampton’s petition thus does not meet the statutory requirements for a second or successive filing. Accordingly, it is ORDERED that his motion for authorization to file the petition is DENIED. Because Lampton had a good-faith basis for claiming that Magwood entitled him to file another § 2255 petition, this matter was not frivolous. That said, we caution Lampton that our prior warning remains in effect: the future filing of any frivolous challenge to his conviction and/or sentence will result in the imposition of sanctions.
. United. States v. Lampton, 158 F.3d 251 (5th Cir. 1998).
. See United States v. Lampton, No. CR. A. 96-125, 2001 WL 263094, at *8 (E.D.La. March 14, 2001) (unpublished) (citing Rutledge v. United States, 517 U.S. 292, 116 S.Ct. 1241, 134 L.Ed.2d 419 (1996)). See generally United States v. Devine, 934 F.2d 1325, 1342 (5th Cir.1991) (“[A] § 846 conspiracy is a lesser-included offense of a § 848 continuing criminal enterprise. Therefore, the Double Jeopardy Clause of the Fifth Amendment bars punishment under both statutes.” (footnote omitted)).
. In re: Billy Lampton, No. 10-30483, slip op. at 2 (5th Cir. Sept. 2, 2010) (per curiam).
. -U.S.-, 130 S.Ct. 2788, 177 L.Ed.2d 592 (2010).
. Magwood, 130 S.Ct. at 2797 (quoting Slack v. McDaniel, 529 U.S. 473, 486, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000)).
. See Leal Garcia v. Quarterman, 573 F.3d 214, 220 n. 32 (5th Cir.2009) (noting that the second-or-successive rules in § 2244, which govern successive petitions under § 2254, should be read in pari materia with those under § 2255” (citing United States v. Orozco-Ramirez, 211 F.3d 862, 864 n. 4 (5th Cir. 2000))); see also Urinyi v. United States, 607 F.3d 318, 321 (2d Cir.2010) (per curiam) ([N]othing in the AEDPA indicates that Congress intended the ‘second or successive rules to operate differently with regard to state and federal prisoners.”).
. Magwood, 130 S.Ct. at 2796 (quoting Panetti v. Quarterman, 551 U.S. 930, 944, 127 S.Ct. 2842, 168 L.Ed.2d 662 (2007)).
. Id. at 2797.
. Id. at 2802.
. See Burton v. Stewart, 549 U.S. 147, 156, 127 S.Ct. 793, 166 L.Ed.2d 628 (2007) (" ‘Final judgment in a criminal case means sentence. The sentence is the judgment. ” (quoting Berman v. United States, 302 U.S. 211, 212, 58 S.Ct. 164, 82 L.Ed. 204 (1937))).
. 130 S.Ct. at 2793.
. No. 11-30319 (5th Cir. June 23, 2011) (per curiam).
. Id., slip op. at 3.
. 398 Fed.Appx. 326, 327 (10th Cir.2010) (unpublished).
. United States v. Buckley, 586 F.2d 498, 505 (5th Cir.1978) (emphasis omitted); accord Devine, 934 F.2d at 1343; United States v. Gon zales, 866 F.2d 781, 786 (5th Cir.1989); United States v. Michel, 588 F.2d 986, 1001 (5th Cir.1979). The Supreme Court adopted the same rule in Ball v. United States, 470 U.S. 856, 864, 105 S.Ct. 1668, 84 L.Ed.2d 740 (1985), and our sister circuits have faithfully applied it, see, e.g., United States v. Snyder, 766 F.2d 167, 171 (4th Cir.1985); United States v. Throneburg, 921 F.2d 654, 657 (6th Cir. 1990).
. United States v. Johnston, 258 F.3d 361, 365 (5th Cir.2001); see also United States v. Hayes, 532 F.3d 349, 352 (5th Cir.2008) (" [A] section 2255 proceeding is civil...” (quoting United States v. Young, 966 F.2d 164, 165 (5th Cir. 1992))).
. See United States v. Richardson, 195 F.3d 316, 317 (7th Cir. 1999) (per curiam) (explaining that a defendant who received two concurrent life sentences following convictions of both conspiracy and CCE “would still be subject to the undisturbed life imprisonment sentence based upon” one conviction even if the other conviction “was permanently set aside”). See generally Devine, 934 F.2d at 1343 n. 6 (characterizing the vacatur of a conspiracy conviction and the 20-year sentence imposed thereon, which was to run concurrently with a life sentence for a CCE conviction, as a "grant [of] little meaningful relief”).
. See Johnson v. United States, 623 F.3d 41, 46 (2d Cir.2010).
. See id. at 46 n. 6.
. Compare supra note 10, with Magwood, 130 S.Ct. at 2802 (conditioning the applicability of its holding on the existence “a new judgment intervening between the two habeas petitions’ ” (quoting Burton, 549 U.S. at 156, 127 S.Ct. 793)).
. See generally Murphy v. United States, 634 F.3d 1303, 1309 (11th Cir.2011) (“Congress’s overriding purpose in enacting AEDPA.... [was] to achieve finality in criminal cases, both federal and state.” (citations and internal quotation marks omitted)).
. See 28 U.S.C. § 2255(h) (A second or successive motion must be certified as provided in section 2244....”); id. § 2244(b)(3)(C) (The court of appeals may authorize the filing of a second or successive application only if it determines that the application makes a prima facie showing that the application satisfies the requirements of this subsection.”).
. 28 U.S.C. § 2255(h)(2). Section 2255(h)(1) authorizes the filing of a second or successive petition that contains newly discovered evidence that, if true, constitutes clear and convincing evidence of actual innocence. Lampton contends that he is factually and/or legally innocent of the CCE offense under our decision in United States v. Bass, 310 F.3d 321 (2002) but he concedes that this claim does not satisfy the requirements of § 2255(h)(1).
. -U.S. •-•, 130 S.Ct. 1473, 176 L.Ed.2d 284 (2010).
. -U.S.-, 130 S.Ct. 2169, 176 L.Ed.2d 979 (2010).