dissenting in part.
Percy Hutton’s jury-instructions claim is procedurally defaulted, as it was not raised on direct appeal in the state courts. Hutton concedes as much.1 Review of that claim is possible, then, only by finding cause and prejudice for the default (which the lead opinion does not do), or by stretching the narrow “fundamental miscarriage of justice” exception far beyond its proper bounds (which the majority does). Not only does that exception to procedural default not apply in this case, but Hutton never even raised the exception in the district court or on appeal, waiving the argument in that court and in this one. The procedural rules that constrain federal-court oversight of state criminal proceedings should not be so lightly brushed aside.
Federal courts generally do not entertain claims that are procedurally barred by an “independent and adequate state procedural rule” unless a valid “cause” excuses the default. Coleman v. Thompson, 501 U.S. 722, 750, 111 S.Ct. 2546, 115 L.Ed.2d 640 (1991). Throughout federal and state post-conviction litigation, Hutton has given only one reason for his failure to present the jury-instructions claim on direct appeal: inefféctíve assistance of appellate counsel. The ineffective-assistance claim is premised on appellate counsel’s failure to raise the jury-instructions issue and trial counsel’s purported ineffectiveness for failing to object to the instructions. As the lead opinion concludes, however, the ineffective-assistance claim warrants no relief, see Lead Op. ante at 500-02, and so that claim cannot excuse Hutton’s default.2
*510That leaves one possible ground for reviewing the' merits of Hutton’s jury-instructions claim: the so-called fundamental-miscarriage-of-justice exception to procedural default, an argument that Hutton has waived. The exception is a narrow one, applying only in “extraordinary case[s].” Gibbs v. United States, 655 F.3d 478, 477 (6th Cir. 2011) (quoting Murray v. Carrier, 477 U.S. 478, 496, 106 S.Ct. 2639, 91 L.Ed.2d 397 (1986)). To obtain a merits review of a constitutional claim, a petitioner asserting this exception must generally show that an “alleged constitutional error has resulted in the conviction of one who is actually innocent of the underlying offense.” Dretke v. Haley, 541 U.S. 386, 388, 124 S.Ct. 1847, 158 L.Ed.2d 659 (2004) (citing Murray, 477 U.S. 478, 106 S.Ct. 2678; Sawyer v. Whitley, 505 U.S. 333, 112 S.Ct. 2514, 120 L.Ed.2d 269 (1992)). In addition to cases involving factual innocence, the exception has been applied in the capital sentencing process, but only to the small subset of cases where a ha-beas “petitioner has shown by clear and convincing evidence that but for constitutional error, no reasonable juror would find him eligible for the death penalty under [state] law.” Sawyer, 505 U.S. at 348, 112 S.Ct. 2514. In such a case, the petitioner can be said to be “innocent” of the death penalty, even if he is factually guilty of the capital crime. But Hutton has never argued, in this court or in the district court, that he is ineligible for the death penalty. He has therefore unquestionably waived the issue. Hutton’s decision not to raise the argument at any point in federal litigation prevents us from analyzing whether he satisfies the fundamental-miscarriage-of-justice exception. See Kuhn v. Washtenaw Cty., 709 F.3d 612, 624 (6th Cir. 2013); see also Foster v. Michigan, 573 Fed.Appx. 377, 392-93 (6th Cir. 2014).
In any event, Hutton had good reason not to argue that exception. Any argument concerning the fundamental-miscarriage-of-justice exception would have been a losing one, as a jury would have been authorized to impose the death penalty if the jury instructions had correctly defined “aggravating circumstances.” The proper inquiry is not whether a defendant is eligible for the death penalty even with the alleged error. Compare Lead Op. ante at 500-01. The exception instead focuses on what would have happened if no error had occurred. The Sawyer Court used the phrase “but for constitutional error,” Sawyer, 505 U.S. at 348, 112 S.Ct. 2514, a phrase that requires courts to ask whether, assuming that no error had occurred, a jury would have been authorized by state law to impose the death penalty.3 In applying that *511standard, Sawyer thus analyzed whether evidence that the state should have furnished to the defendant would have prevented the jury from finding either of the necessary conditions for imposing the death penalty—that the defendant was guilty of the crime and that one or more aggravating circumstances applied. See id. at 349-50, 112 S.Ct. 2514.
Hutton’s eligibility for the death penalty is indisputable. A defendant becomes death-eligible in Ohio when the jury convicts him of a capital murder count with an attached “specification,” as that is the point at which the death penalty is placed on the table. See Wilson v. Mitchell, 498 F.3d 491, 495 & n.2 (6th Cir. 2007). “Imposition of the death penalty for aggravated murder is precluded unless one or more [statutorily defined specifications] is specified in the indictment ... and proved beyond a reasonable doubt.” Ohio Rev. Code § 2929.04(A). A specification is an “eligibility factor” that satisfies the Eighth Amendment’s narrowing requirement. Wilson, 498 F.3d at 505; see also Brown v. Sanders, 546 U.S. 212, 216, 126 S.Ct. 884, 163 L.Ed.2d 723 (2006). In this case, the jury found two such factors—mass murder and felony murder—in the process of convicting Hutton of two counts of aggravated murder. Both factors were included in the indictment. That rendered Hutton eligible for the death penalty.
As there is no question about the validity of the two specifications, any error in the penalty-phase jury instructions did not affect Hutton’s eligibility for the death penalty. The weighing of aggravating circumstances against mitigating evidence does not relate to eligibility. “Once the narrowing requirement has been satisfied, the sentencer is called upon to determine whether a defendant thus found eligible for the death penalty should in fact receive it.” Sanders, 546 U.S. at 216, 126 S.Ct. 884. At sentencing, the jury thus weighs the aggravating circumstances that “the offender was found guilty of committing” against the mitigating evidence. See Ohio Rev. Code § 2929.03(D)(2). (The mass murder and felony murder specifications in Hutton’s indictment doubled as aggravating circumstances for sentencing purposes. See id. § 2929.04(A)(5), (7).) Any infirmity in the instructions on weighing does not negate a defendant’s earlier-determined eligibility.
A hypothetical example demonstrates how this case is different from the type of case that the fundamental-miscarriage-of-justice exception targets. Assume that a defendant was convicted of aggravated murder and that the only aggravating circumstance that the prosecutor argued was an “especially heinous, atrocious, or cruel” factor. At sentencing, the jury weighed that factor against the mitigating evidence en route to the conclusion that the death penalty was warranted. In such a case, the defendant on federal habeas review might be able to show that he was not eligible for the death penalty, allowing the court to reach the merits of his procedurally defaulted claim that an error affected his sentence. That is because the “heinous, atrocious, or cruel” factor is unconstitutionally vague in most applications, see Maynard v. Cartwright, 486 U.S. 356, 364-65, 108 S.Ct. 1853, 100 L.Ed.2d 372 (1988), and no other aggravating circumstances were present in the case. “Sensible meaning is given to the term ‘innocent of the death penalty’ by allowing a showing in addition to innocence of the capital crime itself a showing that there was no aggrava*512ting circumstance or that some other condition of eligibility had not been met.” Sawyer, 505 U.S. at 345, 112 S.Ct. 2514. Because no valid aggravating factors supported the defendant’s death sentence in the hypothetical, the defendant would be “actually innocent” of that penalty. The same cannot be said of this case.
The Supreme Court’s decisions in Hurst v. Florida, — U.S. -, 136 S.Ct. 616, 193 L.Ed.2d 504 (2016), and Ring v. Arizona, 536 U.S. 584, 122 S.Ct. 2428, 153 L.Ed.2d 556 (2002), have nothing to do with whether Hutton is eligible for the death penalty. “[A] claim of ‘actual innocence’ is ... a gateway through which a habeas petitioner must pass to have his otherwise barred constitutional claim considered on the merits.” Gibbs, 655 F.3d at 477 (quoting Herrera v. Collins, 506 U.S. 390, 404, 113 S.Ct. 853, 122 L.Ed.2d 203 (1993)). Hurst and Ring are relevant, if at all, to the merits of Hutton’s claim that constitutional error occurred when the trial judge failed to define the aggravating circumstances. Yet the merits are not reviewable in the context of this case. A federal habeas court has no business reaching a defaulted claim if the petitioner can show neither cause for the default nor that he was innocent of the death penalty.
Even if it were proper to reach the merits, the Supreme Court’s decisions in Hurst and Ring do not require the conclusion that constitutional error occurred. In those cases, state law required a judge, at a separate penalty hearing, to find aggravating circumstances before sentencing a defendant to death. Hurst, 136 S.Ct. at 619; Ring, 536 U.S. at 588, 122 S.Ct. 2428. The Ohio capital system, however, does not work that way. In Ohio, the jury weighs aggravating circumstances and mitigating evidence at sentencing after it has already found the aggravating circumstances at the guilt stage. Here, the jury found the mass-murder and felony-murder circumstances at the guilt phase. Compare Maj. Op. ante at 498-99. What is more, the trial judge in the penalty-phase instructions reminded the jury that it had made those findings, instructing the jury that “[t]he prosecution has the burden to prove beyond a reasonable doubt that the aggravating circumstances, of which the Defendant was found guilty, outweigh the factors in mitigation of imposing the death sentence.” (Emphasis added.) This is therefore not a case in which the jury found no aggravating circumstances, but rather a case in which the jury found aggravating circumstances and later received instructions that did not spell out the aggravating circumstances that the jury had previously found.
That distinction makes all the difference for Sixth Amendment purposes. As we indicated in Webb v. Mitchell, 586 F.3d 383, 399 (6th Cir. 2009), another Ohio death-penalty case, a state-law error in penalty-phase instructions on weighing may be cured by appellate reweighing of the aggravating circumstances and the mitigating evidence. In that case, the state trial judge erroneously instructed the jury at the penalty phase to consider the quantity of the evidence in the weighing analysis rather than the quality. Id. at 397. In rejecting an ineffective-assistance claim, we held that any argument that trial counsel could have raised would not have been a strong one, reasoning that “[t]he Ohio Supreme Court has consistently held that ... ‘careful independent reweighing’ cures errors by the jury or trial court in “weighing the aggravating circumstances against any mitigating factors.’ ” Id. at 399 (quoting State v. Lott, 51 Ohio St.3d 160, 555 N.E.2d 293, 304 (1990)); see also Hoffner v. Bradshaw, 622 F.3d 487, 506 (6th Cir. 2010). Nowhere did we suggest that a penalty-phase error in jury instructions runs afoul of the Ring line of cases. In this case, *513as in Webb, the jury found the aggravating circumstances at the guilt phase, before the error in the penalty-phase instructions. And here, as in Webb, the Ohio Court of Appeals concluded that the death sentence was appropriate after reweighing the aggravating circumstances against the mitigating evidence. See State v. Hutton, 72 Ohio App.3d 348, 594 N.E.2d 692, 694 (1991). There is thus strong reason to doubt the merit of Hutton’s claim.
The judgment of the district court denying Hutton relief should be affirmed. I join all of the lead opinion except Parts II.A and III.
. Judge Merritt contends that there was no procedural default because the Ohio Supreme Court’s silence on Hutton’s claim is a ruling on the merits. Even if the Ohio Supreme Court’s deciding on the merits somehow means there was no default by Hutton, this court cannot presume that the state-court majority dismissed the claim on the merits just because three dissenting justices, discussed the claim, when Hutton did not even raise the claim on his direct appeal to the state court. Furthermore, even if such a presumption were appropriate, it would be overcome in this case. As the lead opinion notes, the state-court majority expressly stated it was not considering the merits of Hutton's; jury-instructions claim. See State v. Hutton, 53 Ohio St.3d 36, 559 N.E.2d 432, 437 n.1 (1990).
. Judge Merritt states that Hutton "suffered ineffective assistance of counsel by both trial *510and appellate counsel so as' to overcome the default.” Merritt Op. ante at 508. Even if defense counsel prejudiced Hutton by defi-ciently failing to object to the jury instruction during the penalty phase of trial, the lead opinion correctly concludes that appellate counsel’s failing to raise an ineffective-assistance claim based on this failure was not deficient, see Lead Op. ante at 501-02. The Ohio Court of Appeals reversed the judgment on five of appellate counsel’s assignments of error. State v. Hutton, No. 51704, 1988 WL 39276, at *6 (Ohio Ct. App. Apr. 28, 1988), rev’d, 53 Ohio St.3d 36, 559 N.E.2d 432 (1990). It cannot be that under these circumstances appellate counsel’s failure to raise one other colorable issue amounts to conduct that is so woefully inadequate as to constitute ineffective assistance. Furthermore, a court must evaluate the objective reasonableness of counsel’s conduct without "the distorting effects of hindsight.” Strickland v. Washington, 466 U.S. 668, 689, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984).
. The Supreme Court in Sawyer also endorsed an Eleventh Circuit decision that stated the same test in different words. That formulation required a petitioner to “show that absent the alleged constitutional error, the jury would *511have lacked the discretion to impose the death penalty.” Sawyer, 505 U.S. at 347 n.15, 112 S.Ct. 2514 (quoting Johnson v. Singletary, 938 F.2d 1166, 1183 (11th Cir. 1991) (en banc)).