
    Sedley ALLEY, Petitioner-Appellee, v. Ricky BELL, Warden, Respondent-Appellant.
    No. 04-5596.
    United States Court of Appeals, Sixth Circuit.
    Argued: June 16, 2004.
    Decided and Filed: Dec. 14, 2004.
    
      ARGUED: Joseph F. Whalen III, Office of the Attorney General, Nashville, Tennessee, for Appellant. Paul R. Bottei, Federal Public Defender’s Office, Nashville, Tennessee, for Appellee. ON BRIEF: Joseph F. Whalen III, Office of the Attorney General, Nashville, Tennessee, for Appellant. Paul R. Bottei, Federal Public Defender’s Office, Nashville, Tennessee, for Appellee.
    Before: BOGGS, Chief Judge; and RYAN and BATCHELDER, Circuit Judges.
   OPINION

BOGGS, Chief Judge.

Sedley Alley, a Tennessee prisoner under sentence of death, filed an unsuccessful petition for a federal writ of habeas corpus. Alley v. Bell, 307 F.3d 380 (6th Cir.2002), cert. denied, 540 U.S. 839, 124 S.Ct. 99, 157 L.Ed.2d 72 (2003); - U.S. -, 124 S.Ct. 1721, 158 L.Ed.2d 406 (2004). His execution was scheduled for June 3, 2004. Mr. Alley then filed an amended motion with the federal district court that had originally denied his habeas petition; this motion requests relief from judgment under Fed.R.Civ.P. 60(b), and/or relief “in the exercise of th[e district] court’s inherent authority” under Article III of the Constitution, and was accompanied by a motion for stay of execution. The district court granted a stay of execution, pending this court’s decision in the en banc case of In re Abdur’Rahman, Nos. 02-6547, 02-6548 (argued Dec. 3, 2003).

The State of Tennessee, on behalf of the respondent, Warden Ricky Bell, has moved us to vacate that stay. For the reasons discussed below, we hold, applying Ab-dur’Rahman, that the district court lacked jurisdiction over Alley’s amended motion, because it is equivalent to a second or successive habeas petition under 28 U.S.C. § 2244(b). We therefore grant the State’s motion to vacate the stay of execution on this basis, and do not address any of the other issues raised in this appeal.

I

In 1985, Suzanne Collins was abducted while jogging near Millington Naval Base, sexually mutilated, and killed. Alley lived on the base, and his car was spotted on the scene shortly after two witnesses heard Collins scream. After Miranda warnings, Alley confessed to having killed Collins while drunk, and led officers back to the scene where the murder took place. He also confessed to having mutilated her with a long, broken-off tree branch, a claim which was consistent with the grave internal injuries that Collins suffered, and led police to the place where the tree limb had been broken off. Alley contended that he did this in order to simulate a sexual assault, and thereby (in his thinking) deflect suspicion from himself. He gave police some other purported details of the killing that were inconsistent with the forensic evidence.

Alley went to trial for Collins’s murder in 1987. He did not contest having committed the act, but instead pursued an insanity defense. He presented evidence that he suffered from a multiple personality disorder, and had committed the murder while under the control of an abnormal personality. Alley sought to offer into evidence videotapes of interview sessions conducted while Alley was under the influence of hypnosis and/or sodium amytal. The trial court excluded this taped evidence on relevance grounds, but allowed Alley to present the testimony of two medical experts who described the interviews, and other evidence, in the course of opining that Alley suffered from insanity.

The jury convicted Alley of kidnapping, aggravated rape, and premeditated first degree murder. The jury then imposed a sentence of death for the murder, and the trial court imposed consecutive forty-year sentences for the remaining two counts. The jury found two aggravating circumstances to justify the punishment of death: the murder was especially heinous, atrocious, or cruel; and Alley committed it during a kidnapping or rape. Alley’s conviction and sentence were upheld on direct appeal. State v. Alley, 776 S.W.2d 506 (Tenn.1989).

Alley then sought post-conviction relief in state court. His post-conviction petition raised claims of judicial bias, challenged a number of the state trial court’s evidentia-ry rulings, asserted that Alley had received ineffective assistance of counsel, and claimed that the Tennessee “heinous, atrocious, or cruel” aggravating instruction read to Alley’s jury at sentencing was unconstitutionally vague. The Tennessee Court of Criminal Appeals affirmed the denial of most of the claims, but ruled that Alley was entitled to an evidentiary hearing on his claims of judicial bias. Alley v. State, 882 S.W.2d 810 (Tenn.Crim.App.1994). The trial court (with a new judge) held an evidentiary hearing, then denied Alley’s petition, and the Court of Criminal Appeals affirmed the denial. Alley v. State, 958 S.W.2d 138 (Tenn.Crim.App.1997), permission to appeal denied, (Tenn. Sept. 29, 1997).

Next, Alley filed a petition for a writ of habeas corpus in federal district court. This petition raised claims that substantially overlapped with the issues in his state postconviction petition. However, Alley argued for the first time in his habe-as petition that the trial court’s exclusion of Alley’s videotaped testimony under hypnosis violated the Confrontation Clause as well as due process. Alley’s habeas petition also included the non-defaulted claim that the “heinous, atrocious, or cruel” (henceforth “HAC”) aggravating instruction was unconstitutionally vague.

The district court denied relief, finding a number of Alley’s claims procedurally defaulted, and denying the rest on the merits. Alley v. Bell, 101 F.Supp.2d 588 (W.D.Tenn.2000). This court granted Alley a certificate of appealability on several issues. On appeal, we affirmed the denial of habeas relief. We upheld the district court’s rulings on procedural default, and, as to the claims that Alley had properly presented to the state courts, we affirmed the district court’s holding that the state courts’ rejection of Alley’s claims was not an unreasonable application of Supreme Court law. Alley, 307 F.3d 380. Alley petitioned for en banc rehearing, which was denied, and certiorari from the Supreme Court, which was also denied, 540 U.S. 839, 124 S.Ct. 99, 157 L.Ed.2d 72 (Oct. 6, 2003). Our mandate, which had been stayed while Alley sought a writ of certiorari, issued on October 27, 2003.

On October 10, 2003, Alley filed a motion in the federal district court for relief from judgment under Fed.R.Civ.P. 60(b). The district court entered an order on November 4, 2003, staying the proceedings on Alley’s motion pending the outcome of the en banc proceeding in In re Abdur’Rakman, Nos. 02-6547, 02-6548 (argued Dec. 3, 2003), involving the question of when a Rule 60(b) motion in a habeas case should be deemed a second or successive habeas petition under 28 U.S.C. § 2244(b). The State apparently responded to this order by requesting the Tennessee Supreme Court to set an execution date for Alley. On January 16, 2004, the Tennessee Supreme Court ordered that Alley’s sentence be carried out on June 3, 2004.

In response, on May 12, 2004, Alley filed with the district court a “First Amended Motion Requesting Relief In the Exercise of This Court’s Inherent Authority, And/Or Relief From Judgment, And/Or Certificate of Appealability,” the filing at issue here, which we will henceforth refer to simply as the “Motion.” As the Motion’s title suggests, it invokes both Rule 60(b), and what are contended to be the district court’s “inherent powers” to grant relief under Article III of the Constitution, as alternative bases for relief.

The Motion disclaims any intention to file or pursue a second or successive habe-as petition, and explicitly objects to the potential recharacterization of the Motion as a second habeas, a form of objection recently sanctioned by the Supreme Court in Castro v. United States, 540 U.S. 375, 124 S.Ct. 786, 157 L.Ed.2d 778 (2003). However, the Motion argues that Alley is entitled to relief from judgment due to a variety of legal and factual developments that occurred after the denial of Alley’s federal habeas petition.

First, it asserts that Alley is entitled to relief because “various legal developments” have demonstrated the error of the district court’s rejection of his constitutional vagueness challenge to the Tennessee HAC aggravator — principally this court’s intervening decision in Cone v. Bell, 359 F.3d 785 (6th Cir.2004), which granted ha-beas relief to a death-sentenced petitioner who challenged the Tennessee HAC instruction given at his trial.

Second, it asserts that Alley is entitled to relief because he “was denied a fair consideration of his Brady claims” due to the withholding of exculpatory evidence in both his state court trial and his federal habeas proceeding. Relief is appropriate under Rule 60(b), Alley argues, in part because this alleged withholding continued during his federal habeas corpus proceedings, and thus constitutes “fraud on the court.” (citing, inter alia, Workman v. Bell, 227 F.3d 331, 335 (6th Cir.2000) (en banc)).

Third, Alley’s Motion asserts that he is entitled to relief on his claim (which the district court previously rejected) that the state trial court unconstitutionally excluded videotaped evidence of Alley’s behavior under hypnosis. Alley argues that the Tennessee Supreme Court’s intervening decision in State v. Carter, 114 S.W.3d 895 (Tenn.2003), which held that it was error to exclude a defendant’s personal correspondence proffered as mitigating evidence, shows that he is entitled to relief from the prior habeas judgment on this basis.

Simultaneously with filing the First Amended Motion, Alley moved for a stay of execution. On May 19, 2004, the district court entered a brief order staying Alley’s execution. It noted that a stay had been granted in Cooey v. Bradshaw, 216 F.R.D. 408 (N.D.Ohio 2003), motion to vacate stay denied, 338 F.3d 615 (6th Cir.2003) (en banc), in part because of the pendency of Ahdur’Rahman and its possible relevance to Cooey’s Rule 60(b) motion. Accordingly, the district judge entered a stay, which, by its terms, was to remain in place until Abdur’Rahman is decided and the district judge has ruled on Alley’s First Amended Motion in light of that decision.

Five days later, the State tendered to this court a motion to vacate the district court’s stay of execution. This motion was filed on May 25. The matter was automatically docketed and assigned to the present panel, which had decided Alley’s original habeas appeal. See 6th Cir. I.O.P. 22(a)(1). In its motion to vacate the stay, the State argued in the alternative. It claimed that if, on one hand, Alley’s Motion was really a second habeas petition, then, under AEDPA, the district court lacked jurisdiction to act on it. Alternatively, if the Motion was properly treated as a Rule 60(b) motion, then it was clearly without merit, making the entry of the stay an abuse of discretion in either case. Against this, Alley argued that the district court’s stay of execution was analogous to the stay upheld by this court en banc in Cooey, and that the Motion, considered as a Rule 60(b) motion, was sufficiently meritorious to deserve full consideration by the district court, especially in light of the pendency of AbdurRahman.

On May 28, this panel entered an order declining to vacate the stay of execution at that time, scheduling the matter for oral argument on June 16, 2004, and requesting supplemental briefing on a number of issues relating to the potential application of Rule 60(b) to Alley’s Motion. The parties filed supplemental briefs addressing these issues.

During oral argument, we also requested (and later received) supplemental briefing on a further issue: whether the federal Anti-Injunction Act, 28 U.S.C. § 2283, barred the federal district court from entering a stay of execution in response to Alley’s Motion for post-judgment relief in this habeas case. As is discussed below, we do not reach that issue.

II

A

We begin instead by considering whether the entry of a stay was jurisdic-tionally proper. In the absence of extraordinary circumstances, we cannot consider the propriety of Alley’s Motion under the standards of Rule 60(b), or the merits of the underlying claims that he seeks to revive, unless the district court’s subject-matter jurisdiction to act as it did is first assured. Steel Co. v. Citizens for a Better Environment, 523 U.S. 83, 101, 118 S.Ct. 1003, 140 L.Ed.2d 210 (1998); id. at 110-11, 118 S.Ct. 1003 (O’Connor, J., concurring). In this case, the underlying substantive questions raised by Alley’s Motion are by no means trivial. Accordingly, no potential exception to the rule that subject-matter jurisdiction must precede other questions is applicable here. See ibid.; Ruhrgas AG v. Marathon Oil Co., 526 U.S. 574, 577, 119 S.Ct. 1563, 143 L.Ed.2d 760 (1999).

More specifically, the question before us is whether Alley’s Motion should have been treated as a second or successive habeas petition under AEDPA. This question implicates subject-matter jurisdiction, because under AEDPA, a petitioner must obtain authorization from the court of appeals “[bjefore a second or successive [habeas] application ... is filed in the district court.” 28 U.S.C. § 2244(b)(3)(A). “From the district court’s perspective,” this provision is “an allocation of subject-matter jurisdiction to the court of appeals,” rather than the district court, over the initial processing of a second or successive habeas petition. United States v. Barrett, 178 F.3d 34, 41 (1st Cir.1999); Nunez v. United States, 96 F.3d 990, 991 (7th Cir.1996); see Robinson v. Johnson, 313 F.3d 128, 138 (3d Cir.2002); Workman v. Bell, 227 F.3d 331, 338 (6th Cir.2000) (en bane) (Siler, J.). Since Alley did not request permission from this court to file his Motion, it follows that, if the Motion is properly viewed as a second or successive habeas, then the district court lacked jurisdiction to consider it, and the stay of execution is invalid.

We recently considered the circumstances in which a post judgment motion should be treated as a second or successive habeas petition in In re AbdurRahman, 392 F.3d 174, 2004 Fed.App. 0428P, 2004 WL 2847749 (6th Cir. Dec. 13, 2004) (en banc). The majority of our court held that a filing counts as a successive habeas petition if its “factual predicate deals primarily with the constitutionality of the underlying ... conviction or sentence .... ” Id. at 181, 2004 WL 2847749, at *6 (quoting Rodwell v. Pepe, 324 F.3d 66, 70 (1st Cir.2003)). On the other hand, if the “factual predicate” of a filing “attacks the manner in which the earlier habeas judgment was procured,” then it falls outside of AEDPA’s limitations on successive habeas petitions — and, in the case of a motion under Rule 60(b), it should be adjudicated pursuant to the normal standards governing Rule 60(b) relief. Id. at 176-77, 2004 WL 2847749 at *1.

At issue in AbdurRahman was the status of a petitioner’s Rule 60(b) motion that asked the district court to vacate its earlier judgment dismissing his habeas petition on procedural default grounds. Abdur’Rah-man’s motion sought reconsideration on the ground that an intervening Tennessee Supreme Court rule had clarified (contrary to the district court’s holding) that he did not need to seek discretionary review from the state supreme court in order to properly preserve his claims of prosecutorial misconduct in the state courts. Id. at 6. Our court held that Abdur’ Rahman’s Rule 60(b) motion was not equivalent to a second or successive habeas petition. It reasoned that the motion simply “relate[d] to the integrity of the federal habeas judgment — and specifically, the basis for the district judge’s procedural default ruling.” Ibid. Furthermore, “[i]f Abdur’Rahman’s motion were granted, it would simply result in the reopening of the federal habeas proceeding, not the vacation of the state criminal judgment.” Id. at 6.

B

Applying the standard adopted in Ab-durRahman, we hold that Alley’s Motion should be classified as a second or successive habeas petition, with respect to each of the claims it contains.

The Motion raises three separate claims for relief. First, Alley argues that he is entitled to relief from the judgment based on this court’s intervening decision in Cone v. Bell, 359 F.3d 785 (6th Cir.2004), which upheld an Eighth Amendment vagueness challenge to the Tennessee HAC instruction in a capital sentencing proceeding. This claim plainly attempts to do the work of a second or successive habeas petition. The ‘Tactual predicate” of this claim is simply Cone itself, and the sole relevance of the Cone decision to the prior habeas proceeding is that it dealt with the same issues as the parallel constitutional vagueness challenge that Alley brought against the use of the HAC instruction in his own trial. (The district court rejected this claim on the merits in the previous habeas proceeding, and it was not encompassed in the certificate of appealability we issued to Alley prior to his appeal in this court.) As such, the Cone claim obviously “presents a direct challenge to the constitutionality of the underlying conviction .... ” AbdurRahman at 6. AEDPA therefore forecloses the district court from considering or acting on it, unless and until Alley satisfies the gatek-eeping criteria of 28 U.S.C. § 2244(b).

Our conclusion that one of Alley’s proposed grounds for Rule 60(b) relief is the functional equivalent of a second or successive habeas petition raises the question of whether we should proceed to consider the status of his other claims. Some of the language of our en banc opinion in Ab-durRahman, and of the opinions of other circuits that we drew upon in reaching our decision, could be read to imply that a putative Rule 60(b) motion should be subjected, in its entirety, to the restrictions that AEDPA places upon successive habe-as petitions, whenever the motion contains at least one claim that is preempted by AEDPA. See AbdurRahman at 6 (“[Wjhen a petitioner presents a direct challenge to the constitutionality of the underlying conviction ... the petition should be treated as a second or successive habeas petition. But if there is no such direct challenge and the petitioner instead challenges the integrity of the district court opinion ... then the district court must treat the motion as one pursuant to Rule 60(b).”) (emphases added); Rodwell, 324 F.3d at 71 (“[A] district judge should treat a Rule 60(b) motion in a habeas case as a second or successive habeas petition whenever the motion threatens to encroach upon precincts patrolled by the AEDPA .... In contrast, if the factual predicate of the motion challenges only the procurement of the federal habeas judgment, it may be adjudicated under Rule 60(b).”) (emphasis added).

However, neither AbdurRahman nor Rodwell actually involved a filing that contained multiple claims. Thus, our court and the First Circuit did not have the chance to consider the proper procedure for such a circumstance. We now hold that when a filing denominated under Rule 60(b) asserts several potential bases for relief, courts should follow a claim-by-claim approach when deciding whether the limitations on successive petitions set out in AEDPA apply to that filing. This claim-by-claim approach was recently embraced by the Third Circuit, in a decision which also employed the same case-by-case, “factual predicate” approach to the interaction of Rule 60(b) and AEDPA that our court adopted in Abdur’Rahmcm. See Pridgen v. Shannon, 380 F.3d 721, 727 (3d Cir.2004). Moreover, this approach fits best with the language of AEDPA, which, in various provisions, mandates a focus on individual “claims” in determining whether the limits imposed by the statute apply. See 28 U.S.C. §§ 2244(b)(1), (b)(2) (providing that “claims” that were presented in a previous habeas petition are subject to dismissal, and that “claims” presented for the first time in a successive habeas are subject to dismissal unless certain gatekeep-ing requirements are met); § 2254(d) (providing that relief cannot be granted based on habeas petition unless state court’s adjudication of a “claim” was unreasonable or contrary to clearly established Supreme Court law). We therefore turn to the remainder of the Motion.

Alley’s second claim is that he is entitled to relief from the judgment rejecting his Brady claim because he has recently discovered, through the use of a private investigator and other inquiries, exculpatory evidence that was not disclosed to him by the State. Alley asserts that this evidence suggests that John Borup, a boyfriend of Corporal Collins at the time of her murder, committed the crime, and accordingly, it would have supported a claim of Alley’s factual innocence of the murder (an argument that he did not pursue at trial).

Alley states that he has recently discovered evidence that Collins’s boyfriend Bor-up matched a description given of a person seen talking with Collins shortly before her abduction; and that he drove a car matching the description of one sighted near the scene. Alley alleges that the State failed to include, in its pretrial disclosures, a report that naval investigators had questioned Borup and that he had no useful information. Alley contends that because it possessed this report, the State must have possessed evidence relating to Borup’s physical description.

Further, Alley states that the State suppressed handwritten notes taken by state pathologist James Bell, who conducted the autopsy of Collins. Bell’s autopsy report was disclosed to Alley’s lawyers, but his notes were not. Bell apparently wrote that Collins could have died from her injuries as late as 1:30 to 3:30 a.m. on the night of the murder. Police had interviewed Alley around midnight on that night, and then released him, keeping him under surveillance for at least part of the time that followed.

Finally, Alley discerns a third example of putative nondisclosure in the trial testimony given by Craig Lahren, a forensic expert who was called by the government. Lahren testified that several hairs were recovered from Collins’s body, and that one of them was determined to have come from an African-American — meaning that it did not match Alley, who is white. Two other hairs recovered from Collins were identified as belonging to a Caucasian. Lahren stated that he was unable to do a fair or successful comparison of these hairs to Alley’s hair. Based on this statement in the record, Alley speculates that Lahren actually performed such a comparison and obtained a result potentially exculpating Alley.

Alley argues that this quasi-.Bra<% claim should be adjudicated under Rule 60(b), rather than as a successive habeas under AEDPA, because the State’s failure to disclose the alleged evidence continued through Alley’s federal habeas proceeding, and therefore constituted fraud on the district court. See Fed.R.Civ.P. 60(b) (stating that limitations of Rule 60 do not alter a district court’s power “to set aside a judgment for fraud upon the court”); Workman v. Bell, 245 F.3d 849, 852 (6th Cir.2001).

We note that the claim of “fraud on the court” that Alley has articulated in connection with his Brady argument in this case is essentially indistinguishable from a standard Brady constitutional claim that is being asserted for the first time after the completion of a first federal habeas proceeding. Such a claim would, as such, be a classic example of a second or successive habeas petition. In his Motion, Alley provides no basis for concluding that the attorneys representing the State in federal court carried out a deliberate or reckless fraud on the federal district court, except for a pair of conclusory assertions that the evidence that was not produced to him at trial was also “withheld ... throughout the prior proceedings in [the district] [c]ourt.” Motion at 3; see id. at 28. In his filings before this court, Alley has attempted to supplement this allegation slightly. He points to the fact that an Assistant District Attorney General who represented the State of Tennessee during Alley’s state posi-eonviction proceedings also made a special appearance at one point in Alley’s federal habeas case. This, however, is insufficient to make out a sufficient allegation of fraud on the federal habeas court, and thereby bring Alley’s Brady challenge out of the ambit of AED-PA and into that of Rule 60(b). While a Brady violation can be established by the mere inadvertent nondisclosure of material exculpatory evidence in a petitioner’s state criminal trial, Spirko v. Mitchell, 368 F.3d 603, 610 (6th Cir.2004) (citing Strickler v. Greene, 527 U.S. 263, 281-82, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999)), fraud on the court requires a showing that an officer of the court whose judgment is under attack acted in a manner that is “intentionally false, wilfully blind to the truth, or is in reckless disregard for the truth.” Workman, 245 F.3d at 852. Here, even if we assume that the putative nondisclosures raised by Alley could satisfy the Brady standards with respect to his state trial, his allegations do not provide any “factual predicate” for the claim that the state attorneys who litigated the prior habeas proceeding recklessly or wilfully concealed those matters from the federal district court. Accordingly, Alley’s factual allegations cannot be said to impugn the manner in which the federal habeas judgment was procured, and these late-raised Brady claims are therefore subject to the limitations of AEDPA rather than Rule 60(b). Cf. Abdur’Rahman at 6.

Finally, Alley’s Motion asserts that he is entitled to relief from the judgment rejecting his claim that his trial violated due process and the Eighth Amendment because the trial judge excluded, from both the guilt and sentencing phases of trial, certain proffered evidence that Alley suffered from a multiple personality disorder. The trial judge excluded videotapes of interviews conducted with Alley under hypnosis, concluding that these tapes were likely to confuse a lay jury. However, he allowed Alley to bring this material before the jury in another form, by presenting the testimony of two medical experts describing his condition. The experts testified that they had viewed the tapes of Alley’s hypnotic states and that they confirmed a diagnosis of multiple personality disorder.

Both the federal district court and this court rejected Alley’s claim that the exclusion of the tapes unconstitutionally impaired his right to present a defense, see, e.g., Rock v. Arkansas, 483 U.S. 44, 107 S.Ct. 2704, 97 L.Ed.2d 37 (1987); Cham bers v. Mississippi, 410 U.S. 284, 93 S.Ct. 1038, 35 L.Ed.2d 297 (1973), or his right to present mitigating evidence at capital sentencing, Lockett v. Ohio, 438 U.S. 586, 98 S.Ct. 2954, 57 L.Ed.2d 973 (1978). Echoing the district court, we noted that the Tennessee Supreme Court had affirmed the trial court’s ruling that the videotapes were inadmissible. Alley, 307 F.3d at 393-94; see State v. Alley, 776 S.W.2d 506-516 (Tenn.1989). We concluded that since the trial court had allowed Alley to present the information in question to the jury in a slightly different format than the one he sought to employ, and it had not applied the relevant state evidentiary law in a “mechanical, arbitrary, or disproportionate” manner, the Tennessee court’s resolution of the issue was not unreasonable or contrary to Lockett. 307 F.3d at 399.

Alley now contends that he is entitled to relief from this judgment because of the Tennessee Supreme Court’s intervening decision in State v. Carter. Carter held that the state trial court had erred by excluding from the defendant’s capital sentencing hearing evidence of cards, letters, and poems that he had sent to his pastor, which the defendant sought to introduce as mitigating evidence of good character. The trial court excluded the items on the ground that they duplicated the pastor’s testimony. The Tennessee Supreme Court reversed (though it went on to hold the error harmless), emphasizing that Tennessee law provides for “the liberal admission of mitigation evidence in the penalty phase and ensures that a jury will have as much information as possible in making its sentencing determination.” 114 S.W.3d at 905. That court did not call into question its prior decision in Alley, or indicate that Tennessee law had been altered in this respect.

We have considerable doubt as to whether Alley, in this portion of his Motion, has articulated any sort of claim for relief, let alone a proper claim for relief from judgment, independent of a constitutional claim, that would escape the strictures of AEDPA. To the extent that Alley asserts that an erroneous application of state law at his sentencing proceedings requires postjudgment relief, this cannot present any basis for action, since our court has no authority to revisit the Tennessee Supreme Court’s application of Tennessee evidentiary law to the facts of this case. Alley, 307 F.3d at 398 & n. 6. And to the extent Alley argues that Carter bolsters the merits of the Lockett claim in his habeas petition, he is arguing that his conviction is infirm on federal constitutional grounds — which means that his present claim is subject to the limitations of AED-PA. The Eighth Amendment cases springing from Lockett employ a special concept of “constitutionally relevant mitigating evidence,” Buchanan v. Angelone, 522 U.S. 269, 276, 118 S.Ct. 757, 139 L.Ed.2d 702 (1998); DePew v. Anderson, 311 F.3d 742, 744 (6th Cir.2002), that is not reducible to the question of whether state relevance law has been obeyed. Accordingly, if Alley’s claim invoking Carter is to be construed as having any possible substance, then it must be construed as a claim that “deals primarily with the constitutionality of the underlying ... sentence,” Abdur’Rahman at 5 (quoting Rodwell, 324 F.3d at 70). Accordingly, it, too, should be treated as an attempt to do the work of the second or successive habeas petition.

Ill

Alley also argues that the district court is empowered to grant him relief from judgment under “the exercise of [its] inherent authority” under “Article III of the United States Constitution.” Motion, p.l. He contends that, to the extent that AED-PA, 28 U.S.C. § 2244(b), is construed to divest the district court of jurisdiction to grant him the relief he requests, it is unconstitutional.

These arguments are clearly inapposite in the present context. As we have discussed in Part II above, Alley’s claims are substantially equivalent to successive requests for a writ of habeas corpus. Congress possesses broad powers to regulate the availability of habeas corpus relief. If any constitutional provision acts as a limit to AEDPA and/or Rule 60(b) here, it is the Suspension Clause, U.S. Const, art. I, § 9, el. 2. And the contours of this clause are wide enough to accommodate the limits Congress imposed on successive habeas relief in AEDPA. The Supreme Court demonstrated this in Felker v. Turpin, 518 U.S. 651, 116 S.Ct. 2333, 135 L.Ed.2d 827 (1996), which unanimously upheld, against a Suspension Clause challenge, AEDPA’s new jurisdictional limits on the filing and adjudication of successive habeas petitions in the federal district courts. As relevant to Alley’s argument here, the Court explained:

[AEDPA] requires a habeas petitioner to obtain leave from the court of appeals before filing a second habeas petition in the district court. But this requirement simply transfers from the district court to the court of appeals a screening function which would previously have been performed by the district court as required by 28 U.S.C. § 2254 Rule 9(b). The Act also codifies some of the preexisting limits on successive petitions, and further restricts the availability of relief to habeas petitioners. But we have long recognized that “the power to award the writ by any of the courts of the United States, must be given by written law,” Ex parte Bollman, 4 Crunch 75, 94, 2 L.Ed. 554 (1807), and we have likewise recognized that judgments about the proper scope of the writ are “normally for Congress to make.” Lonchar v. Thomas, 517 U.S. 314, 323, 116 S.Ct. 1293, 1298, 134 L.Ed.2d 440 (1996).
The new restrictions on successive petitions constitute a modified res judicata rule, a restraint on what is called in habeas corpus practice “abuse of the writ.” In McCleskey v. Zant, 499 U.S. 467, 111 S.Ct. 1454, 113 L.Ed.2d 517 (1991), we said that “the doctrine of abuse of the writ refers to a complex and evolving body of equitable principles informed and controlled by historical usage, statutory developments, and judicial decisions.” Id. at 489, 111 S.Ct. at 1467. The added restrictions which the Act places on second habeas petitions are well within the compass of this evolutionary process, and we hold that they do not amount to a “suspension” of the writ contrary to Article I, § 9.

Id. at 664. Turpin straightforwardly requires us to reject Alley’s Article III argument here.

IV

Thus, if Aley’s Motion is anything, it is a second or successive habeas petition. Accordingly, the district court lacked jurisdiction to consider it — and thus, a fortiori, to enter a stay of execution. 28 U.S.C. § 2244(b)(3)(A). In this circuit, the usual course of action when a petitioner improperly files a successive habeas petition with the district court is to transfer the filing to a panel of this court to apply the gatekeeping criteria of § 2244(b) to it. In re Sims, 111 F.3d 45 (6th Cir.1997). However, since Aley has explicitly objected to the characterization of his Motion as a habeas petition (a procedure sanctioned by the Supreme Court in Castro v. United States, 540 U.S. 375, 124 S.Ct. 786, 792, 157 L.Ed.2d 778 (2003)), we conclude that the proper course of action is to remand, for the limited purpose of permitting Aley either to withdraw his motion, or to allow the district court to transfer it to a panel of our court for application of the gatekeeping criteria of AEDPA.

Accordingly, the entry of the stay of execution is VACATED. The case is REMANDED for the limited purpose just stated. 
      
      . We accordingly reject the approach of some cases, e.g., Hess v. Cockrell, 281 F.3d 212, 214-15 (5th Cir.2002), in which the court proceeded to consider whether a Rule 60(b) motion filed by a previously unsuccessful ha-beas petitioner satisfied the standards for relief under Rule 60(b), without first determining that the motion was not the equivalent to a second or successive habeas petition.
     