OPINION

BOGGS, Circuit Judge.

More than twelve years ago, Antonio Franklin, an Ohio prisoner sentenced to death, filed a petition for a writ of habeas corpus in federal district court. The district court denied Franklin's petition on the merits and this court affirmed. Five months later, Franklin moved the district court for relief from judgment pursuant to Federal Rule of Civil Procedure 60(b), seeking to avail himself of the Supreme Court's decisions in Martinez v. Ryan, ___ U.S. ___, 132 S.Ct. 1309, 182 L.Ed.2d 272 (2012), and Trevino v. Thaler, ___ U.S. ___, 133 S.Ct. 1911, 185 L.Ed.2d 1044 (2013). The district court denied Franklin's motion on the merits and Franklin again appealed. As we explain, Franklin's Rule 60(b) motion is a "second or successive" habeas application that the district court lacked jurisdiction to consider without prior authorization from this court. Because Franklin has not satisfied the gatekeeping requirements applicable to motions for authorization to file a "second or successive" habeas application, he is not entitled to relief.

I

A

As an adolescent, Antonio Franklin moved into the Dayton, Ohio, home of his grandparents and uncle in order to escape his alcoholic mother's physical and verbal abuse. Despite the abuse, Franklin appeared to be a relatively well-adjusted child. As Franklin approached the age of seventeen, however, his behavior began to change. On one occasion, for example, Franklin expressed a fear that extraterrestrials would abduct him. On another, he showed up at his girlfriend's mother's house in the middle of a winter night, appearing to be dazed and confused. Franklin also began to abuse marijuana at around this time, causing a rift between himself and his grandparents.

On April 17, 1997, when Franklin was nineteen years old, his grandparents and uncle informed him that he would soon have to find his own place to live. The discussion apparently upset Franklin. Later that evening, Franklin and his uncle got into an argument about Franklin's use of the family's phone, which his uncle followed by making a joke that implied that Franklin was sexually attracted to men. Franklin responded by picking up a baseball bat and attacking his uncle. Franklin then turned on his grandmother and grandfather. After severely beating all three of the relatives who had taken him in, Franklin seized a gun and shot his grandmother in the head, killing her. Franklin then set fire to the house, leaving his grandfather and uncle to die. With his grandmother's jewelry in his pocket, Franklin fled to Tennessee in his grandfather's vehicle. He was promptly apprehended by Tennessee police and confessed his involvement in the killings, which he said he had committed because his uncle had raped him as a child.

Franklin was eventually returned to Ohio, where he faced six counts of aggravated arson, two counts of aggravated robbery, and six counts of aggravated murder. Franklin pleaded not guilty by reason of insanity to all counts and also claimed that he was incompetent to stand trial. After holding a pretrial competency hearing, however, the trial court found that Franklin was in fact competent and that his case could proceed to trial. During trial, Franklin engaged in various forms of disruptive and inappropriate behavior. In addition to flashing gang signs at the jury, belching loudly, and repeatedly interrupting the judge:

Appellant's Br. 15-16 (citations omitted). In the face of overwhelming evidence of Franklin's guilt, the jury found Franklin guilty of all fifteen counts and recommended that he receive the death penalty. The trial court agreed with the jury's recommendation and sentenced Franklin to death.

On direct appeal, Franklin argued that his trial attorneys were ineffective for failing to request a new competency hearing in the middle of the trial. In particular, Franklin argued that his "behavior during trial should have prompted defense counsel to request another competency determination to decide if he was competent to continue at the trial and penalty phases," noting that "during the sentencing portion of Appellant Franklin's trial, defense counsel informed the trial court that Appellant Franklin was unable to assist them because of his mental state during the trial." In another section of his appellate brief, in which Franklin argued that the trial court should have ordered a midtrial competency hearing sua sponte, Franklin also noted that Dr. Eugene Cherry, a psychologist whom Franklin called as an expert witness at trial, "consistently testified that Appellant Franklin suffered from ... paranoid schizophrenia."

The Ohio Supreme Court affirmed, holding that a midtrial competency hearing was not warranted. See State v. Franklin, 97 Ohio St.3d 1, 776 N.E.2d 26, 35 (2002). The court held that Dr. Cherry's testimony concerning Franklin's schizophrenia "did not need to be reconsidered [by the trial court] because similar testimony had been presented at [Franklin's] pretrial competency hearing." Ibid. The court noted that although Franklin's courtroom actions "did indeed constitute strange behavior, they illustrated a pattern of rudeness rather than incompetency to stand trial." Ibid. For this reason, the Ohio Supreme Court concluded that "the evidence ... does not shed any new light on [Franklin's] ability to understand the proceedings, to interact with his counsel, or to assist in his defense." Ibid. After determining that "no [competency] hearing was warranted," id. at 40, the court held that counsel could not be ineffective for failing to request a second competency hearing, id. at 39-40. The United States Supreme Court denied certiorari. Franklin v. Ohio, 539 U.S. 905, 905, 123 S.Ct. 2249, 156 L.Ed.2d 115 (2003) (mem.).

While his direct appeal was still pending in the Ohio Supreme Court, Franklin, who was still represented by counsel, filed a petition for postconviction relief in state trial court in which he repeated his direct-appeal claim that his trial attorneys were ineffective for failing to request a midtrial competency hearing. Ohio has a bifurcated system for processing constitutional claims arising out of a criminal trial. If an alleged constitutional error can be raised and fully litigated on direct appeal, res judicata generally bars the relitigation of that alleged error in a state postconviction proceeding. See, e.g., State v. Sowell, 73 Ohio App.3d 672, 598 N.E.2d 136, 141-42 (1991). But if the claim of constitutional error is supported by sufficient extra-record evidence, res judicata does not prohibit a prisoner from raising the alleged error again on state collateral review. State v. Cole, 2 Ohio St.3d 112, 443 N.E.2d 169, 171 (1982). As the district court explained below, "an Ohio defendant may raise an ineffective assistance of trial counsel claim on direct appeal and get a decision on the merits of that claim, based on the evidence of record, and then get more evidence that was not in the record and re-file the claim in post-conviction."

Unlike his direct-appeal ineffective-assistance-of-trial-counsel claim, which relied wholly on evidence in the record, Franklin supported his state postconviction claim with new evidence, namely, an affidavit from a new psychologist, Dr. Sharon Pearson, who stated that based on her review of the record, including a video recording of trial, Franklin was not competent during his trial; an affidavit from Suzanne Wynn, who assisted defense counsel and observed strange behavior from Franklin; and an affidavit from his lead trial counsel, who stated that Franklin was unable to assist in his own defense. The state trial court, however, rejected Franklin's petition without a hearing, explaining that his ineffective-assistance-of-trial-counsel claim did not include extra-record evidence. Since it was not so raised, it was barred by res judicata because it could be raised only on direct appeal.

The Ohio Court of Appeals affirmed the trial-court decision, addressing Franklin's ineffective-assistance-of-trial-counsel argument on the merits. The court explained that because Franklin's attorneys "had already argued Franklin's incompetency to the trial court and lost," they had "no reason to believe [that] they would be successful on a second attempt, [and] it was a reasonable tactical decision to refrain from requesting a new hearing." State v. Franklin, No. 19041, 2002 WL 1000415, at *4 (Ohio Ct. App. May 17, 2002). The court further explained that "Franklin has [also] failed to establish that he was prejudiced." Ibid. The Ohio Supreme Court denied Franklin's petition for review. State v. Franklin, 108 Ohio St.3d 1475, 842 N.E.2d 1054, 1054 (2006) (mem.).

B

Having exhausted state-court remedies, Franklin timely filed an application for a writ of habeas corpus in the United States District Court for the Southern District of Ohio. In addition to arguing that the trial court erred by failing to conduct a new competency hearing sua sponte, Franklin claimed that his trial attorneys had been ineffective for their failure to seek "another competency hearing when [Franklin] was unable to assist them or maintain decorum during the guilt phase of trial." Although Franklin's habeas application was governed by the provisions of the Antiterrorism and Effective Death Penalty Act of 1996 ("AEDPA"), Pub. L. No. 104-132, 110 Stat. 1214, the district court conducted an evidentiary hearing in accordance with the prevailing law prior to Cullen v. Pinholster, 563 U.S. 170, 131 S.Ct. 1388, 179 L.Ed.2d 557 (2011). At the hearing, Franklin called his trial lawyers, who testified that Franklin was not "mentally, emotionally [or] intellectually at the trial" and could not assist in his defense. The attorneys recounted that Franklin was unable to communicate with them inside or outside of court, had no reaction to the guilty verdict whatsoever, and expressed confusion when the trial judge pronounced a death sentence.

The district court denied Franklin's habeas application in 2009. After considering the evidence it heard at the hearing, the district court concluded that Franklin had not satisfied his burden of showing that the Ohio Supreme Court's "determination that it was rudeness rather than incompetence that explained his strange behavior during his trial was an `unreasonable determination of the facts in light of the evidence presented in the State court proceeding.'" The district court followed the Ohio Supreme Court's reasoning that because Franklin's demeanor at trial did not impose upon the trial judge a duty to hold a second competency hearing, counsel could not have been ineffective for failing to request one.

We affirmed in a unanimous decision. See Franklin v. Bradshaw, 695 F.3d 439, 457 (6th Cir. 2012). In light of the Supreme Court's then-recent decision in Pinholster, we explained that because Franklin's ineffective-assistance claim "was raised on direct appeal and Franklin abandoned the post-conviction version of this claim, see Robinson v. Jones, 142 F.3d 905, 906 (6th Cir. 1998), he can only rely on the record evidence that was before the Ohio Supreme Court on direct appeal." Franklin, 695 F.3d at 452. In other words, because the Pinholster decision suggested that the district court erred by holding a hearing, id. at 451, 452 n.3, we could not rely on the evidence introduced in federal court to adjudge the reasonableness of the relevant state-court decisions. Issues "not raised on appeal[ ] are considered abandoned and not reviewable on appeal." Robinson, 142 F.3d at 906. On appeal to us, Franklin decided not to mention the Ohio Court of Appeals's adjudication of his ineffective-assistance claim, or to rely on evidence that he brought before the state postconviction courts in conjunction with that claim. See Appellant's Br. 53-55, in Franklin, 695 F.3d 439, (No. 09-3389). Thus, we measured the reasonableness of the Ohio Supreme Court's decision with respect to the evidence before it. See Franklin, 695 F.3d at 452.

Upon undertaking that review, we concluded that the evidence in the state-court record suggested that "Franklin was competent. There was no reason to hold a second competency hearing." Ibid. For this reason, we held that "[t]he Ohio Supreme Court's rejection of [Franklin's ineffective-assistance-of-trial-counsel] claim was neither contrary to, nor an unreasonable application of, clearly established Supreme Court precedent, was not based on an unreasonable determination of the facts in light of the evidence presented, and was not clearly erroneous." Ibid. "Franklin," we explained, "fail[ed] to demonstrate prejudice." Ibid. The Supreme Court denied Franklin's petition for a writ of certiorari. Franklin v. Robinson, ___ U.S. ___, 133 S.Ct. 1724, 1724, 185 L.Ed.2d 789 (2013) (mem.).

Two months after denying certiorari in Franklin's case, the Supreme Court decided Trevino v. Thaler, ___ U.S. ___, 133 S.Ct. 1911, 185 L.Ed.2d 1044 (2013), which expanded the Court's holding in Martinez v. Ryan, ___ U.S. ___, 132 S.Ct. 1309, 182 L.Ed.2d 272 (2012). In Martinez, the Supreme Court qualified another earlier decision, Coleman v. Thompson, 501 U.S. 722, 111 S.Ct. 2546, 115 L.Ed.2d 640 (1991), and held that:

Martinez, 132 S.Ct. at 1320 (emphasis added). The following year, in Trevino, the Supreme Court held that the rule of Martinez also applies where "[t]he structure and design of the [state] system in actual operation ... make[s] it `virtually impossible' for an ineffective assistance claim to be presented on direct review." Trevino, 133 S.Ct. at 1915 (quoting Robinson v. State, 16 S.W.3d 808, 810-11 (Tex. Crim. App. 2000)).

A few months after the Supreme Court decided Trevino, Franklin, who was — and still is — represented by counsel, filed a motion for relief from judgment pursuant to Federal Rule of Civil Procedure 60(b)(6). Apparently drawing on our observation that Franklin had "abandoned the post-conviction version of" his ineffective-assistance claim, Franklin, 695 F.3d at 452, Franklin argued that "the postconviction version" of that claim was an independent and procedurally defaulted claim that this court never considered on the merits due to Coleman. See Coleman, 501 U.S. at 752-54, 111 S.Ct. 2546 (holding that ineffective assistance of state postconviction counsel is not cause that would excuse a procedural default). In Franklin's view, "[b]ecause [state] post conviction counsel's failure was in effect a denial of ... assistance," Martinez and Trevino would now excuse that procedural default, enabling this court to consider the merits of his ineffective-assistance claim. What is more, because the ineffective-assistance claim brought on state postconviction review was "never adjudicated on the merits," Franklin claimed that Pinholster "presents no bar to review of the claim using the evidence" presented in the federal evidentiary hearing.

The district court denied the motion on the ground that Franklin's ineffective-assistance claim was not procedurally defaulted and that therefore neither Martinez nor Trevino applied. The court explained that Franklin had already "received consideration of the merits of that claim" on direct review in the Ohio Supreme Court, and was "precluded from merit consideration of the claim in post-conviction" not "by any procedural default of post-conviction counsel, but by Ohio's res judicata doctrine." Having concluded that Martinez and Trevino would not allow Franklin to relitigate his claim in federal court, the district court concluded that Franklin had not shown entitlement to relief under Rule 60(b)(6). As a result, the court found no reason to "decide whether [Franklin's] [m]otion is effectively a second or successive habeas petition." Franklin timely appealed.

II

We review a district court's decision to deny a Rule 60(b) motion for abuse of discretion. Stokes v. Williams, 475 F.3d 732, 735 (6th Cir. 2007) (per curiam). We recognize an "abuse of discretion" when our review leaves us with "a definite and firm conviction that the trial court committed a clear error of judgment." Burrell v. Henderson, 434 F.3d 826, 831 (6th Cir. 2006) (quoting Amernational Indus., Inc. v. Action-Tungsram, Inc., 925 F.2d 970, 975 (6th Cir. 1991)). Relief under Rule 60(b) is the exception, not the rule, and we are guided by the constraints imposed by a "public policy favoring finality of judgments and termination of litigation." Waifersong, Ltd. Inc. v. Classic Music Vending, 976 F.2d 290, 292 (6th Cir. 1992). Particularly strict standards apply to motions made pursuant to Rule 60(b)(6), under which a court may grant relief "only in exceptional or extraordinary circumstances" where principles of equity "mandate" relief. Olle v. Henry & Wright Corp., 910 F.2d 357, 365 (6th Cir. 1990) (quoting Hopper v. Euclid Manor Nursing Home, Inc., 867 F.2d 291, 294 (6th Cir. 1989)). As we explain, however, we need not inquire into the district court's exercise of discretion in this case because our independent review of the record points squarely to the conclusion that the district court lacked jurisdiction to consider Franklin's motion at all.

III

As mentioned above, Rule 60(b) allows a civil litigant the opportunity to seek relief from a final judgment and request a federal district court to reopen his case under limited circumstances. See Fed. R. Civ. P. 60(b). AEDPA, which applies to Franklin's case, does not "expressly circumscribe the operation of Rule 60(b)." Gonzales v. Crosby, 545 U.S. 524, 529, 125 S.Ct. 2641, 162 L.Ed.2d 480 (2005). But the statute's restrictions on federal courts' ability to consider and grant prisoners' applications for a writ of habeas corpus indirectly limit Rule 60(b)'s operation in the habeas corpus context: the effect of AEDPA is that "Rule 60(b), like the rest of the Rules of Civil Procedure, applies in habeas corpus proceedings under 28 U.S.C. § 2254 only `to the extent that [it is] not inconsistent with' applicable federal statutory provisions and rules." Gonzalez, 545 U.S. at 529, 125 S.Ct. 2641 (alteration in original) (quoting Rules Governing Section 2254 Cases in United States District Court, R. 11, 28 U.S.C. § 2254); see also Rules Governing Section 2254 Cases in United States District Court, R. 12, 28 U.S.C. § 2254.

Those "applicable federal statutory provisions and rules" sharply restrict federal courts' ability to consider and grant "second or successive" habeas petitions. See 28 U.S.C. § 2244(b). Relevant here, any claim that has already been adjudicated in a previous petition must be dismissed. Id. § 2244(b)(1). Any claim that has not been adjudicated must also be dismissed unless "it relies on either a new and retroactive rule of constitutional law or new facts showing a high probability of actual innocence." Gonzalez, 545 U.S. at 529, 125 S.Ct. 2641 (citing 28 U.S.C. § 2244(b)(2)). Lastly, federal district courts lack jurisdiction to consider second or successive habeas petitions without preauthorization from the relevant Court of Appeals. 28 U.S.C. § 2244(b)(3); Burton v. Stewart, 549 U.S. 147, 149, 127 S.Ct. 793, 166 L.Ed.2d 628 (2007) (per curiam). Because "Rule 60(b) motions ... may not be used as vehicles to circumvent the[se] limitations that Congress has placed upon the presentation of claims in a second or successive application for habeas relief," Moreland v. Robinson, 813 F.3d 315, 322 (6th Cir. 2016), our threshold inquiry is whether Franklin's Rule 60(b) motion is a "true" Rule 60(b) motion or simply a "second or successive" habeas application cloaked in Rule 60(b) garb. Gonzalez, 545 U.S. at 531, 125 S.Ct. 2641.

Case law provides us with some guidance in delineating the boundary between the two. A petitioner's Rule 60(b) motion is a "second or successive" habeas application "when it `seeks vindication of' or `advances' one or more `claims.'" Post v. Bradshaw, 422 F.3d 419, 424 (6th Cir. 2005) (quoting Gonzalez, 545 U.S. at 531-32, 125 S.Ct. 2641). A "claim," in turn, "is `an asserted federal basis for relief from a state court's judgment of conviction.'" Ibid. (quoting Gonzalez, 545 U.S. at 530, 125 S.Ct. 2641). For example, a habeas petitioner's Rule 60(b) motion advances claims "when [the petitioner] seeks to add a new ground for relief or seeks to present `new evidence in support of a claim already litigated.'" Moreland, 813 F.3d at 322 (quoting Gonzalez, 545 U.S. at 531, 125 S.Ct. 2641). By contrast, a petitioner does not seek to advance new claims "when [his] motion `merely asserts that a previous ruling which precluded a merits determination was in error — for example, a denial for such reasons as failure to exhaust, procedural default, or statute-of-limitations bar.'" Post, 422 F.3d at 424 (quoting Gonzalez, 545 U.S. at 532 n.4, 125 S.Ct. 2641).

Applying these rules to Franklin's Rule 60(b) motion, it is clear that Franklin's Rule 60(b) motion "advances" an "asserted federal basis for relief from a state court's judgment of conviction." Gonzalez, 545 U.S. at 530, 125 S.Ct. 2641. The general thrust of Franklin's motion for relief from judgment is that neither this court nor the district court considered evidence introduced at Franklin's federal evidentiary hearing when adjudicating his ineffective-assistance claim. See Appellant's Jan. 28, 2016, Letter Br. 1-3. In other words, having lost on that claim in both courts, Franklin seeks a new opportunity to argue that claim with new evidence that apparently reveals his trial attorneys' alleged ineffectiveness. Ibid. But as we have held, a prisoner seeking relief under Rule 60(b) brings a "second or successive" habeas application when he "seeks to present `new evidence in support of a claim already litigated.'" Moreland, 813 F.3d at 323 (quoting Gonzalez, 545 U.S. at 531-32, 125 S.Ct. 2641). Because Franklin's Rule 60(b) motion does just that, the district court lacked jurisdiction to consider the new iteration of his ineffective-assistance claim without prior authorization from this court. See Burton, 549 U.S. at 149, 127 S.Ct. 793.

Franklin protests that he is not seeking to attack this court's on-the-merits resolution of his ineffective-assistance claim, but rather this court's determination that the postconviction version of his ineffective-assistance claim was procedurally defaulted. See Appellant's Jan. 28, 2016, Letter Br. 1-2. As we have recounted, Franklin views the postconviction version of his ineffective-assistance claim as an independent claim that we previously declined to consider on the ground that it was procedurally defaulted. Ibid. If this is true, Franklin posits, his Rule 60(b) motion attacks not this court's merits adjudication of his direct-appeal ineffective-assistance-of-trial-counsel claim, but rather this court's determination that the postconviction ineffective-assistance-of-trial-counsel claim was procedurally defaulted in state court. Ibid. And if that is true, it is arguable that Martinez and Trevino would excuse Franklin's procedural default, paving the way for a merits consideration of his postconviction ineffective-assistance-of-trial-counsel claim. Appellant's Br. 35.

Franklin's argument suffers from several defects, two of which are particularly relevant here. As a preliminary matter, although Franklin purports to use his Rule 60(b) motion to attack this court's reliance on a state procedural bar to foreclose federal review of the postconviction version of his ineffective-assistance claim, we declined to consider that version of the claim due to Franklin's federal-court default, not a state-court one. Indulging for a moment Franklin's view that the postconviction version of his claim is an independent claim, this court did not hold that the postconviction ineffective-assistance claim was procedurally defaulted due to Franklin's failure to overcome Ohio's res judicata bar. (Indeed, in adjudicating that claim on postconviction review, the Ohio Court of Appeals did not rely on res judicata and instead addressed that claim on its merits. See Franklin, 2002 WL 1000415, at *4.) As mentioned above, in reviewing the district court's denial of Franklin's first habeas petition, we cited our decision in Robinson v. Jones, 142 F.3d 905 (6th Cir. 1998), to explain that because Franklin had not relied on evidence he offered to the state postconviction court in support of his ineffective-assistance claim in this court, we would gauge the reasonableness of the Ohio Supreme Court's earlier adjudication of his ineffective-assistance claim on direct appeal, not the Ohio Court of Appeals's adjudication of the claim on postconviction review. See Franklin, 695 F.3d at 452.

Equally important is that Franklin's postconviction claim of ineffective assistance of trial counsel is not an independent claim; Franklin is merely offering additional support for a claim that he already litigated. Although it is possible that there are instances when new evidence transforms an old claim into a new one, see Pinholster, 563 U.S. at 186 n.10, 131 S.Ct. 1388, the Supreme Court has long cautioned us to draw a distinction between the "presentation of additional facts" and "the substance of [a petitioner's] claim." Vasquez v. Hillery, 474 U.S. 254, 257-58, 106 S.Ct. 617, 88 L.Ed.2d 598 (1986). The former sufficiently alters the latter to create a "new" claim for purposes of 28 U.S.C. § 2244(b)(1) only where the "gravamen of [a petitioner's] argument" is different. Babbitt v. Woodford, 177 F.3d 744, 746 (9th Cir. 1999) (per curiam); accord In re Hill, 715 F.3d 284, 294 (11th Cir. 2013); In re West, 402 Fed.Appx. 77, 79 (6th Cir. 2010); Felder v. McVicar, 113 F.3d 696, 698 (7th Cir. 1997). Simply put, for purposes of AEDPA, "[n]ew evidence does not usually give rise to a new claim; it merely provides additional proof of a claim already adjudicated on the merits." Pinholster, 563 U.S. at 216, 131 S.Ct. 1388 (Sotomayor, J., dissenting).

Assuming for the sake of argument that Martinez and Trevino do apply in Ohio — and that those decisions would allow Franklin to circumvent Pinholster in the manner that he hopes, but see Moore v. Mitchell, 708 F.3d 760, 784 (6th Cir. 2013) (rejecting an Ohio prisoner's argument that Martinez permits the introduction of new evidence for an ineffective assistance of counsel claim on habeas review despite the Court's holding in Pinholster) — the gravamen of the argument that Franklin seeks to present in federal court now is no different than that of the argument that he presented in his appeal from the district court's denial of his habeas application. Then, as now, Franklin relied on the same "nucleus of operative facts," Brannigan v. United States, 249 F.3d 584, 590 (7th Cir. 2001) (Cudahy, J., concurring in the judgment), namely, that his trial attorneys should have requested a new competency hearing upon witnessing his bizarre behavior at the time of his trial. The fact that he now offers more evidence in support of that ultimate conclusion does not change matters; "we will not consider new factual grounds in support of the same legal claim that was previously presented." Babbitt, 177 F.3d at 746. For purposes of 28 U.S.C. § 2244(b)(1), then, Franklin's Rule 60(b) motion does not present a "new" claim.

Our preliminary inquiry is, of course, not whether Franklin has satisfied the threshold requirements of 28 U.S.C. § 2244(b), but rather whether his Rule 60(b) motion is in substance a "second or successive" habeas petition subject to those requirements. Indeed, a Rule 60(b) filing that satisfies the requirements of 28 U.S.C. § 2244(b) may still be a "second or successive" habeas petition. But in this case, where it is clear that Franklin's Rule 60(b) motion presents a claim that would not satisfy those requirements, 28 U.S.C. § 2244(b) illustrates just why Franklin's filing exceeds the limits of a "true" Rule 60(b) motion. Gonzalez, 545 U.S. at 531, 125 S.Ct. 2641. As the Supreme Court has made clear, Rule 60(b) applies to habeas petitioners "only `to the extent that [it is] not inconsistent with' applicable federal statutory provisions and rules," including 28 U.S.C. § 2244(b)(1). Gonzalez, 545 U.S. at 529, 125 S.Ct. 2641 (alteration in original) (quoting 28 U.S.C. § 2254 R. 11 (2004)). For this reason, "[a] habeas petitioner's [Rule 60(b)] filing" that seeks to present "newly discovered evidence" in support of a claim may be "at least similar enough [to a habeas corpus application] that failing to subject it to the same requirements would be `inconsistent with'" AEDPA. Id. at 531, 125 S.Ct. 2641 (quoting 28 U.S.C. § 2254 R. 11 (2004)).

At the very least, then, if we are to avoid rendering 28 U.S.C. § 2244(b)(1) entirely nugatory, Franklin may not use Rule 60(b) as a vehicle for relitigating the same "claim" that was already decided against him in a previous habeas petition. See 28 U.S.C. § 2244(b)(1); Gonzalez, 545 U.S. at 531, 125 S.Ct. 2641. Because Franklin seeks to do just that with his claim-splitting theory, we must construe his filing as a "second or successive" habeas application subject to the threshold requirements set forth in 28 U.S.C. § 2244(b). And, as we have explained, because district courts lack jurisdiction to consider "second or successive" habeas applications without prior authorization from the appropriate Court of Appeals, see 28 U.S.C. § 2244(b)(3); Burton, 549 U.S. at 149, 127 S.Ct. 793, the district court erred by reaching the merits of Franklin's filing in the absence of any such authorization from this court.

IV

Our holding that Franklin's Rule 60(b) motion is in substance a "second or successive" habeas application that the district court lacked jurisdiction to consider does not end our inquiry. In like situations, we generally construe a prisoner's appellate brief as making a request for authorization to file a second or successive habeas application and proceed to determine whether the prisoner has satisfied the threshold requirements for such authorization. See, e.g., Moreland, 813 F.3d at 325; In re Bowling, 422 F.3d 434, 435 (6th Cir. 2005). Franklin, however, has not met those prerequisites. An application for permission to file a "second or successive" habeas petition may not be granted on any claim that was raised in a previous habeas petition. 28 U.S.C. § 2244(b)(1). As we have already explained, because the new evidence of Franklin's attorneys' ineffectiveness in no way alters the gravamen of his previous claim, his instant claim is simply a new variation on an old claim that he raised in his first petition. See Babbit, 177 F.3d at 746. Accordingly, we may not grant Franklin leave to file a second or successive habeas application under the terms of 28 U.S.C. § 2244(b)(1). See In re West, 402 Fed.Appx. at 79.

V

Congress enacted AEDPA with the purpose of furthering the finality of state-court criminal convictions. Williams v. Taylor, 529 U.S. 420, 436, 120 S.Ct. 1479, 146 L.Ed.2d 435 (2000). As a result, "AEDPA does not suffer kindly the relitigation of tired claims." In re Fowlkes, 326 F.3d 542, 548 (4th Cir. 2003) (Gregory, J., concurring in the judgment). Because Franklin's Rule 60(b) motion represents an effort to relitigate a claim that this court already resolved in the Warden's favor, the motion is in substance a "second or successive" petition that the district court lacked authority to adjudicate without prior authorization from this court. See Burton, 549 U.S. at 157, 127 S.Ct. 793; Gonzalez, 545 U.S. at 534-35, 125 S.Ct. 2641. And because Franklin cannot satisfy the gatekeeping requirements for "second or successive" habeas applications, see 28 U.S.C. § 2244(b), we must deny him such authorization. For these reasons, we VACATE the district court's order for want of jurisdiction, and DENY Franklin's request for authorization to file a second or successive habeas petition.