
680 F.3d 596 (2012)
Donald Wayne STROUTH, Petitioner-Appellant,
v.
Roland COLSON, Warden, Respondent-Appellee.
No. 08-6116.
United States Court of Appeals, Sixth Circuit.
Argued: April 17, 2012.
Decided and Filed: May 23, 2012.
*599 ARGUED: Jerome C. Del Pino, Federal Public Defender's Office, Nashville, Tennessee, for Appellant. James E. Gaylord, Office of the Attorney General, Nashville, Tennessee, for Appellee. ON BRIEF: Jerome C. Del Pino, Henry A. Martin, Federal Public Defender's Office, Nashville, Tennessee, Mark E. Olive, Tallahassee, Florida, for Appellant. James E. Gaylord, Office of the Attorney General, Nashville, Tennessee, for Appellee.
Before: SUTTON, COOK and KETHLEDGE, Circuit Judges.

OPINION
SUTTON, Circuit Judge.
Thirty-four years ago, a jury convicted Donald Strouth of first-degree murder for killing James Keegan during a robbery of Keegan's used-clothing store in Kingsport, Tennessee. The jury sentenced Strouth to death, a sentence the Tennessee appellate courts affirmed on direct appeal and in two collateral-review proceedings. Strouth sought a writ of habeas corpus in federal district court, asserting sixteen grounds for relief. The district court denied the petition. We affirm.

I.
On February 15, 1978, Keegan's wife found her husband's dead body on the floor of his clothing store. The seventy-year-old man's throat had been slit "from ear to ear." Strouth v. State (Strouth IV), 999 S.W.2d 759, 761 (Tenn.1999). The State charged Strouth and Jeffrey Dicks with robbery and murder, trying them separately to avoid the possibility that either one might be unconstitutionally prejudiced by his co-defendant's inculpatory statements to the police. See Bruton v. United States, 391 U.S. 123, 88 S.Ct. 1620, 20 L.Ed.2d 476 (1968). The evidence at trial "tended to show that Strouth had been the person who actually cut Keegan's throat": witnesses saw blood on Strouth's hands and clothes shortly after the murder; the medical examiner testified that blood spots on Strouth's pants were consistent with his having stood over Keegan and cut his throat; Strouth's girlfriend testified he had confessed to the robbery and said that during it, "Jeff froze on me"; and Keegan's wound could have been inflicted by a hawkbill knife that Strouth's girlfriend had given him. Strouth IV, 999 S.W.2d at 761. The police also found various items missing from Keegan's store in Strouth's possession, and a friend of Strouth's testified that Strouth had confessed to killing a man. Strouth v. State (Strouth II), 755 S.W.2d 819, 827 (Tenn. Crim.App.1986).
The jury convicted Strouth of robbery with a deadly weapon and felony murder. In the penalty phase of the trial, the jury found two aggravating circumstances beyond a reasonable doubt: that the murder was "heinous, atrocious or cruel" and that Strouth murdered Keegan in the process of committing a robbery. State v. Strouth (Strouth I), 620 S.W.2d 467, 469 (Tenn. 1981). The Tennessee Supreme Court affirmed *600 Strouth's murder conviction and death sentence. Id. at 473.
The following year, Strouth petitioned the state trial court for postconviction relief, claiming ineffective assistance of counsel during the guilt and penalty phases of the trial. The Court of Criminal Appeals denied Strouth's petition, and the Tennessee Supreme Court denied leave to appeal. Strouth II, 755 S.W.2d at 819, 833; see Strouth IV, 999 S.W.2d at 762. In 1988, Strouth filed a federal habeas petition. Four years later, while that petition was still before the district court, the Tennessee Supreme Court held that when a jury convicts a defendant of capital felony murder, the State may not use the underlying felony as an aggravating circumstance. State v. Middlebrooks, 840 S.W.2d 317, 346 (Tenn.1992), superseded in part by statute, see State v. Reid, 91 S.W.3d 247, 306 n. 13 (Tenn.2002). Strouth asked the district court to hold his petition in abeyance while he pursued a Middlebrooks claim in state court, but the district court dismissed his petition without prejudice.
Back in state court, Strouth prevailed on his Middlebrooks claim. It was an empty victory. The court deemed the error harmless, reasoning that the jury would have imposed the same death sentence based on the other aggravating circumstance in the casethat the murder was heinous, atrocious or cruel. Strouth IV, 999 S.W.2d at 763-67. Strouth raised several other new challenges to his conviction and sentence, involving jury instructions and allegedly withheld evidence, but the Court of Criminal Appeals rejected these claims too, Strouth v. State (Strouth III), No. 03C01-9507-CC00195, 1997 WL 90636, at *7-10 (Tenn.Crim.App. Mar. 4, 1997), and the Tennessee Supreme Court declined to review them, see Strouth IV, 999 S.W.2d at 763.
Strouth filed a new federal habeas petition in 2000. Applying the Antiterrorism and Effective Death Penalty Act (AEDPA), the district court denied Strouth's petition but granted a certificate of appealability on most of his claims.

II.
At the outset, we must decide whether AEDPA governs Strouth's case (the State's position) or whether pre-AEDPA law applies (Strouth's position). Strouth filed his first federal habeas petition in 1988, but the district court dismissed it without prejudice to permit Strouth to exhaust his claims in state court. After Strouth exhausted his claims, he filed a new federal petition in 2000, four years after AEDPA went into effect.
AEDPA applies to "[a]n application for a writ of habeas corpus," and the deference required by the statute applies to "any claim that was adjudicated on the merits in State court." 28 U.S.C. § 2254(d). Consistent with this language, the Supreme Court has held that when a "federal habeas corpus application [is] not filed until after AEDPA's effective date, that application is subject to AEDPA's amendments." Woodford v. Garceau, 538 U.S. 202, 210, 123 S.Ct. 1398, 155 L.Ed.2d 363 (2003) (emphasis added); cf. Lindh v. Murphy, 521 U.S. 320, 336, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997) (holding that AEDPA applies to petitions filed after its effective date, not to petitions pending on its effective date). There is just one habeas application in this instance, and it was filed four years after AEDPA's 1996 effective date. The 1988 petition cannot be the relevant application because it no longer exists. The effect of dismissing a complaint without prejudice, as the district court did here, is to "treat [it] as if it never existed." Hull v. Kyler, 190 F.3d 88, 103 (3d Cir.1999).
*601 Strouth's 2000 habeas petition not only included new claims in the sense that some of them had now been reviewed by the state courts, but it also included new claims altogetherclaims unrelated to the 1988 petition. Were we to accept his invitation to apply pre-AEDPA standards to his 2000 petition, we either would give him an undeserved windfall (by allowing new post-1996 claims to be assessed under pre-AEDPA law) or would be forced to bifurcate this one application into two (by treating some of it as filed before 1996 and some of it as after). There is no precedent for either approach.
Every circuit to address this question has held that AEDPA governs the later application. See Sacco v. Cooksey, 214 F.3d 270, 273 (2d Cir.2000) (per curiam); Hull, 190 F.3d at 103-04; Taylor v. Lee, 186 F.3d 557, 559-60 (4th Cir.1999); Tassin v. Cain, 517 F.3d 770, 776 & n. 18 (5th Cir.2008); Sanchez v. Gilmore, 189 F.3d 619, 622-23 (7th Cir.1999); Ryan v. Clarke, 387 F.3d 785, 789 (8th Cir.2004); Chapman v. LeMaster, 302 F.3d 1189, 1193-94 (10th Cir.2002). Other courts, including ours, have not explicitly taken the question head on but have applied AEDPA in situations like this one, where the state prisoner filed an unexhausted claim before 1996 and an exhausted claim later. See, e.g., Johnson v. Bell, 525 F.3d 466, 473 (6th Cir.2008); James v. Ryan, 679 F.3d 780, 800-02 (9th Cir.2012); Blankenship v. Hall, 542 F.3d 1253, 1270-71 & n. 3 (11th Cir.2008).
Strouth's response to all of this is not to offer a different construction of the language or to identify contrary precedents. He instead makes a practical pointthat the district court could have held his petition in abeyance while he exhausted his claims rather than dismissed the petition without prejudice. Whether AEDPA applies, he adds, "should not turn on which federal district judge is assigned to a case and whether he or she keeps the case on the docket or chooses not to do so." Br. at 61. It is not that simple. True, the Supreme Court has endorsed the "stay-and-abeyance" practice in order to protect diligent prisoners from running afoul of AEDPA's one-year statute of limitations through no fault of their own. See Rhines v. Weber, 544 U.S. 269, 276-79, 125 S.Ct. 1528, 161 L.Ed.2d 440 (2005). But, in doing so, it noted that the practice, "if employed too frequently, has the potential to undermine" AEDPA's "twin purposes" of finality and efficiency in federal habeas. Id. at 277, 125 S.Ct. 1528. As a result, the Court concluded, stay and abeyance "should be available only in limited circumstances" when dismissal without prejudice would likely thwart any opportunity for federal review of a diligent prisoner's potentially meritorious claims. Id. That is not the problem here, as no one claims that the procedure used by the district court created (or avoided) a limitations problem.
AEDPA applies. To prevail, Strouth thus must demonstrate that the state courts' resolution of his claims "resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States." 28 U.S.C. § 2254(d)(1).

III.

A.
Ineffective assistance (guilt phase). Strouth says he received ineffective assistance of counsel during the guilt phase of his trial because his attorney "failed to interview critical prosecution witnesses and, consequently, to impeach their testimony." Br. at 64-65. He focuses on the testimony of three witnesses: Barbara *602 Davis (Strouth's girlfriend, who testified that Strouth admitted to participating in the robbery); Betty Dicks (wife of Jeffrey Dicks, Strouth's co-defendant, who testified that Strouth told her he slit Keegan's throat); and Jeffrey McMahan (an acquaintance of Strouth, who testified that shortly after the murder Strouth confessed to killing someone). Had his attorney properly interviewed these witnesses ahead of time, Strouth contends, he would have uncovered substantial impeachment evidence. That would have included the following: Davis agreed to testify only because the police threatened to prosecute her as an accomplice; Betty Dicks was determined to implicate Strouth in order to deflect blame from her husband and went so far as to offer sex and money to McMahan for favorable testimony; and Strouth previously told McMahan made-up stories about killing people, calling into question the truth of the confession.
To get anywhere on this claim, Strouth must show that his attorney performed unreasonably and that his poor representation prejudiced the case. Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). In holding that Strouth satisfied neither requirement, see Strouth II, 755 S.W.2d at 825-27, the Court of Criminal Appeals emphasized his shortcomings in meeting the second prongthat he "has not shown a reasonable probability that any of the witnesses could have testified differently but for counsel's conduct in failing to interview all witnesses prior to trial, or that significant impeachment testimony was lost thereby." Id. at 827. The court pointed out that none of the testimony would "negate the physical evidence, including recovery of the items taken from the store, the stolen cash, and Strouth's blood-spattered jeans"; that there is no evidence Davis's trial testimony was coerced; and that the jury knew Betty Dicks was Jeffrey Dicks's wife and hence partial toward him, so any further impeachment on that point would have been of little value. Id. at 826-27.
This reasoning neither contradicts nor unreasonably applies Supreme Court case law. Other than Strickland, Strouth does not cite a single Supreme Court case to support his argument, an omission that does not by itself doom the claim but that underscores a difficult reality. It is not easy to satisfy Strickland through the failure to impeach prosecution witnesses when the impeachment evidence is weak and cumulative, and the evidence of the defendant's guilt is "overwhelming," all true here, Strouth II, 755 S.W.2d at 833. See, e.g., United States v. Munoz, 605 F.3d 359, 381-82 (6th Cir.2010); Davis v. Booker, 589 F.3d 302, 309 (6th Cir.2009); Hodge v. Haeberlin, 579 F.3d 627, 646 (6th Cir. 2009); Moore v. Parker, 425 F.3d 250, 253 (6th Cir.2005).
Strouth's court-of-appeals citations do not improve matters. For one thing, none of them was an impeachment case; they involved claims that defense counsel should have called witnesses favorable to the defense who never testified. For another thing, each decision involved undiscovered witnesses who would have undercut a key part of the government's case. See Ramonez v. Berghuis, 490 F.3d 482, 489 (6th Cir.2007) (trial "boil[ed] down to a credibility contest" between complainant and defendant, and witnesses would have corroborated defendant's account of the facts); Towns v. Smith, 395 F.3d 251, 260 (6th Cir.2005) (witness would have testified that other people committed the crime, where there were "notable weaknesses in the prosecution's case," which rested entirely on one eyewitness); Groseclose v. Bell, 130 F.3d 1161, 1166, 1170 (6th Cir. 1997) (trial counsel failed to call any witnesses, introduce any evidence, or develop *603 a theory of the case even though the evidence linking the defendant to the crime was "relatively weak"). The same cannot be said here. As the state courts recognized, Strouth's new impeachment evidence was marginal at best and the evidence of his guilt was strong at the least. The district court properly rejected this claim.

B.
Ineffective assistance (penalty phase). As to the penalty phase of the trial, Strouth argues his attorney should have done more: (1) hired an expert to perform a mental-health evaluation of Strouth, which allegedly would have revealed evidence of brain damage and mental illness; (2) investigated his troubled upbringing and family problems; (3) investigated his criminal records in North Carolina to rebut the State's introduction of that evidence in support of an aggravating circumstance; and (4) emphasized Strouth's youth as a mitigating circumstance. We disagree.
1. Mental-health evaluation. While litigating his first petition for postconviction relief in state court, Strouth sought state funding to develop expert testimony about his mental health. The court denied his request. Strouth II, 755 S.W.2d at 821. In reviewing that decision, the Court of Criminal Appeals reasoned that Strouth waived the mental-health issue by not raising it on direct appeal. Id. at 822. Nor did ineffective assistance of appellate counsel excuse the waiver, the court held, as Strouth could not show prejudice because he made "no showing" of what a mental-health evaluation "would have turned up that might have affected the outcome of the sentencing hearing." Id. This was not an unreasonable application of Supreme Court law, which requires a State to fund a psychiatric evaluation only when the defendant's mental health is "likely to be a significant factor in his defense." Ake v. Oklahoma, 470 U.S. 68, 82-83, 105 S.Ct. 1087, 84 L.Ed.2d 53 (1985).
Strouth tried to revive the claim in his second petition for postconviction relief in state court. The Court of Criminal Appeals rejected it, holding that the Middlebrooks error (involving the felony-murder aggravating circumstance) did not change the court's earlier analysis. Strouth III, 1997 WL 90636, at *6 n. 4; see also Strouth IV, 999 S.W.2d at 767.
In his federal habeas petition, Strouth seeks to "supplement[]" the record with "expert evaluations of his longstanding mental illness." Br. at 99-100. But in reviewing the state court's resolution of Strouth's claim, federal courts must "limit[]" themselves to "the record that was before the state court." Cullen v. Pinholster, 563 U.S. ___, 131 S.Ct. 1388, 1398, 179 L.Ed.2d 557 (2011). The new mental-health evidence has no bearing on whether AEDPA permits us to grant him habeas relief on this claim. And because that is the only ground on which Strouth seeks relief with respect to this claim, the claim necessarily fails. Even if that were not the case, the district court's reasoning on this score independently suffices to reject this claim: recent mental evaluations offer little insight into Strouth's state of mind twenty-five-plus years ago, as the state courts reasonably concluded in finding no prejudice.
2. Troubled upbringing and family problems. Strouth argues his attorney failed him during the penalty phase by declining to investigate his childhood. Strouth notes he was raised in a troubled area of Maryland by a single mother who was "constantly yelling at her children" and sometimes resorted to corporal punishment. *604 Br. at 9. He did not fit in well at school, he adds, and frequently ran away from home, and the authorities eventually placed him in a state children's facility.
The state courts reasonably applied Supreme Court precedent in rejecting this claim. Strouth, for starters, "refused to let counsel call his mother to testify about his difficulties as a child." Strouth II, 755 S.W.2d at 828. It is difficult to investigate an area to which the client refuses access. Even then, Strouth's upbringing, forlorn though it was in several respects, does not reflect the kind of extreme abuse and deprivation found in other cases. See, e.g., Wiggins v. Smith, 539 U.S. 510, 535, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003) (petitioner "suffered physical torment, sexual molestation, and repeated rape" during childhood); Sowell v. Anderson, 663 F.3d 783, 792 (6th Cir.2011) (petitioner's infant brother died of starvation; his father repeatedly beat him and sexually molested his sister, threatening to burn her alive if she reported it; he and his siblings were bitten by rats and infected with worms); Foust v. Houk, 655 F.3d 524, 539-44 (6th Cir.2011) (petitioner lived in a home with "uninhabitable living conditions," including feces smeared on the wall, vomit on the floor, piles of garbage and dirty laundry stacked throughout the home, and insect and rodent infestation; he and his siblings regularly suffered brutal beatings; his brothers raped his sisters and threatened them with death). In cases involving childhood experiences of a degree similar to Strouth's, we have not found Strickland prejudice stemming from an attorney's failure to introduce the evidence at sentencing. See, e.g., West v. Bell, 550 F.3d 542, 556 (6th Cir.2008); Owens v. Guida, 549 F.3d 399, 414 (6th Cir.2008). That is particularly true when, as was the case here, "the brutality" of the murder "would have completely overwhelmed" any mitigation evidence stemming from a difficult childhood. Tibbetts v. Bradshaw, 633 F.3d 436, 445 (6th Cir.2011). The state courts reasonably rejected this claim.
3. Prior criminal history. Strouth argues his attorney should have presented evidence that his prior criminal history was not as severe as the State's evidence led the jury to believe. But, as the Court of Criminal Appeals recognized, that is beside the point because the jury rejected the State's request to find Strouth's criminal history to be an aggravating factor at sentencing. Strouth II, 755 S.W.2d at 827. The only valid remaining aggravating factorthat the murder was heinous, atrocious or cruelhas nothing to do with Strouth's criminal history. A defendant cannot suffer prejudice from his attorney's success in preventing evidence from being used as an aggravating factor or from his failure to put on more evidence of this ilk when it has nothing to do with the remaining aggravating factor.
4. Youth. Strouth argues that his attorney should have emphasized his relative youth as a mitigating factor. In rejecting the claim, the Tennessee Supreme Court held that the theory would not have changed matters:
The fact that Strouth was nineteen at the time of the killing carries no great mitigation weight since the record reflects that Strouth had been living independent of his parents, traveling routinely between Tennessee and North Carolina, and committing crimes as a juvenile. This is not the picture of a dependent teenager, nor does it demonstrate an innocent young man whose inexperience in criminal matters may have led him into an unlawful situation.
Strouth IV, 999 S.W.2d at 767. Strouth cites no Supreme Court case that contradicts this analysis or that the Tennessee *605 court unreasonably applied. Nor can we think of one. The claim fails.

C.
Strouth argues the trial court erred in permitting the State to introduce evidence at the penalty phase that reflected badly on his character but was not linked to any aggravating or mitigating circumstance. The State responds that the claim is procedurally defaulted because Strouth failed to raise it on direct appeal. We disagree. A claim is not procedurally defaulted for federal habeas purposes where the most recent state court opinion addressing the claim reaches the merits rather than invoking a procedural bar. See Ylst v. Nunnemaker, 501 U.S. 797, 801, 111 S.Ct. 2590, 115 L.Ed.2d 706 (1991). The Tennessee Court of Criminal Appeals discussed whether Strouth's claim was procedurally barred, it is true. But the court declined to resolve the question, reaching the merits instead. See Strouth II, 755 S.W.2d at 829-30. We must do the same.
In rejecting the claim on the merits, the Court of Criminal Appeals concluded that, although it "may have been error to allow testimony about Strouth's boasts of criminal activity and about his juvenile record," the error was "not of such magnitude that it requires reversal." Id. at 830. Any error was one of state evidence law. It would give rise to a federal constitutional claim only if the state court based its death sentence on "factors ... totally irrelevant to the sentencing process" in violation of the Eighth Amendment, Johnson v. Mississippi, 486 U.S. 578, 585, 108 S.Ct. 1981, 100 L.Ed.2d 575 (1988), or if the error "was so pervasive as to have denied [Strouth] a fundamentally fair trial," in violation of the Due Process Clause of the Fourteenth Amendment, Apanovitch v. Houk, 466 F.3d 460, 487 (6th Cir.2006). The alleged error did neither. The Court of Criminal Appeals emphasized that "the jury found two aggravating circumstances related to the crime itself and no mitigating circumstance to counterbalance them." Strouth II, 755 S.W.2d at 830. The evidence the jury consideredof relatively minor crimes Strouth had committed in the past and implausible boasts of criminal activitydoes not call its verdict into question. See Banks v. Dretke, 540 U.S. 668, 700-01, 124 S.Ct. 1256, 157 L.Ed.2d 1166 (2004).

D.
Strouth argues the prosecution committed misconduct during the penalty phase of his trial when it (1) emphasized the death penalty's deterrent effect, (2) suggested to the jury the law required a death sentence and (3) told the jury that "no one is asking you to kill anyone." Br. at 126-33. Strouth suggests AEDPA does not apply because the state courts failed to resolve these claims on the merits. Not true: the state courts resolved each claim on the merits. See Strouth I, 620 S.W.2d at 472-73; Strouth II, 755 S.W.2d at 832; Strouth III, 1997 WL 90636, at *7.
Strouth invokes Caldwell v. Mississippi, which overturned a death sentence after the prosecutor led the jury to believe that the final decision whether to condemn the defendant rested with the state supreme court. 472 U.S. 320, 323, 105 S.Ct. 2633, 86 L.Ed.2d 231 (1985). Caldwell does not apply retroactively to cases on collateral review. See Sawyer v. Smith, 497 U.S. 227, 245, 110 S.Ct. 2822, 111 L.Ed.2d 193 (1990). But even if it did, the Court of Criminal Appeals reasonably concluded that Caldwell "addresses a different type of argument" and any error "was of a minor nature and harmless beyond a reasonable doubt." Strouth II, 755 S.W.2d at 832; see Fry v. Pliler, 551 U.S. *606 112, 121-22, 127 S.Ct. 2321, 168 L.Ed.2d 16 (2007). That is particularly so given the other parts of the prosecution's closing argument that emphasized the importance of the jury's role in the process. See Strouth App'x at 1420.
Strouth's other prosecutorial-misconduct claimsthat the State wrongfully emphasized deterrence and suggested the law required a death sentencefare no better. The Tennessee Supreme Court evaluated the prosecution's closing argument andreasonably in our viewfound it to be "within the bounds of reason." Strouth I, 620 S.W.2d at 473; see also Strouth III, 1997 WL 90636, at *7. Prosecutorial misconduct not linked to a constitutional guarantee violates the Due Process Clause only if it renders the defendant's trial fundamentally unfair. Donnelly v. DeChristoforo, 416 U.S. 637, 645, 94 S.Ct. 1868, 40 L.Ed.2d 431 (1974). That did not happen. A prosecutor may refer to the policy rationales behind a State's decision to make the death penalty available. See Irick v. Bell, 565 F.3d 315, 325 (6th Cir.2009). And a prosecutor has no less right to discuss a jury's duty to impose the death penalty if legally warranted than a defense counsel has the right to discuss a jury's duty to acquit (or give a life sentence) if legally warranted. See Hicks v. Collins, 384 F.3d 204, 219 (6th Cir.2004); Tenn.Code Ann. § 39-13-204(f)-(g).

E.
Strouth argues his death sentence must be reversed because the one remaining valid aggravating circumstance the jury foundthat his murder "was especially heinous, atrocious, or cruel in that it involved torture and depravity of mind," Strouth I, 620 S.W.2d at 469is unconstitutionally vague. See Abdur'Rahman v. Bell, 226 F.3d 696, 709-11 (6th Cir.2000). But the Tennessee Supreme Court has adopted a narrowing construction that cures the constitutional defect, holding that this aggravating circumstance is directed to "the conscienceless or pitiless act of a defendant which is unnecessarily tortuous to the victim, or evinces a depraved state of mind." Strouth IV, 999 S.W.2d at 766.
These new adjectives add little, Strouth responds, as they too are "unconstitutionally vague." Br. at 142. One problem with this argument is that the Supreme Court has approved Tennessee's narrowing construction against a similar vagueness challenge. See Bell v. Cone, 543 U.S. 447, 455-57, 125 S.Ct. 847, 160 L.Ed.2d 881 (2005). Another problem, indeed a worse problem, is that the Court invoked Strouth's case in doing so, explaining that the Tennessee Supreme Court permissibly adopted a narrowing construction of the law in his appeal. Id. at 457, 125 S.Ct. 847. All of this makes it exceedingly difficult to maintain that the Tennessee courts unreasonably applied, much less contradicted, decisions of the United States Supreme Court.

F.
Strouth argues the state trial court violated due process when it excluded expert statistical testimony on the deterrent effect of the death penalty. Strouth invokes two cases to support his argument, but neither one gets the job done. In Gardner v. Florida, the Court reversed a death sentence based in part on confidential information in a presentence report not accessible by the defendant. 430 U.S. 349, 351, 97 S.Ct. 1197, 51 L.Ed.2d 393 (1977) (plurality opinion). Strouth likens his case to Gardner in that the trial court allowed the prosecution in closing to highlight the deterrent effect of the death penalty but denied him the right *607 to present statistical evidence on the same point. The comparison is inapt. The prosecution in this case did not seek to use confidential evidence or indeed any evidence at all to make this point; it simply mentioned deterrence in open court during a closing argument. Nothing prevented Strouth's attorney, during his closing argument, from arguing that the death penalty has little or no deterrent effect. Strouth and the State shared equal footing in what the court allowed, and did not allow, them to do.
As for the other case, Lockett v. Ohio, 438 U.S. 586, 98 S.Ct. 2954, 57 L.Ed.2d 973 (1978), it allows a defendant to introduce in mitigation "any aspect of a defendant's character or record and any of the circumstances of the offense that the defendant proffers as a basis for a sentence less than death." Id. at 604, 98 S.Ct. 2954 (plurality opinion). Statistical evidence about the deterrent effect of the death penalty does not fit this description. It has nothing to do with the "defendant's character, prior record, or the circumstances of his offense." See id. at 604-05 n. 12, 98 S.Ct. 2954. We see no error in the state courts' resolution of this issue, permitting both sides to discuss deterrence in general terms during closing argument but not permitting either to introduce evidence on the point. A defendant has no constitutional right to present evidence on any topic that might arise at closing. See Wright v. Bell, 619 F.3d 586, 599-601 (6th Cir.2010).

G.
Strouth argues the State violated Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), when it failed to give the defense evidence that (1) Jeffrey Dicks or someone else killed Strouth, and (2) witnesses against Strouth were biased or coerced. The Court of Criminal Appeals twice held that this evidence is neither favorable to Strouth nor material under Brady because there was no reasonable probability of a different result even if Strouth had introduced the evidence at trial. Strouth II, 755 S.W.2d at 828; Strouth III, 1997 WL 90636, at *9.
That conclusion is a reasonable one, as the evidence is equivocal or factually dubious, or both. Here is the evidence: an eyewitness saw Dicks with fresh blood on his shoe shortly after the time of the killing; a polygraph test showed that Dicks's answers were "indicative of deception"; Barbara Davis and Betty Dicks were not credible witnesses, see supra at 602; and a police report "identified suspects who admitted to killing [Keegan] in connection to a conspiracy by the Ku Klux Klan to kill homosexuals." Strouth Br. at 149-51. Evidence that Dicks, a co-defendant, had blood on his shoes suggests only that he was at the scene of the murder, not that he was the one who slit Keegan's throat. Evidence that Dicks's polygraph test indicated deception, aside from being inadmissible in Tennessee courts, see Irick v. State, 973 S.W.2d 643, 652-53 (Tenn. Crim.App.1998), suggests only that he sought to conceal his involvement in the crime, hardly unusual behavior for a co-defendant, not that he played a more central role in the crime than Strouth did. The "allegations about Barbara Davis and Betty Dicks were not supported by the record," and at any rate were not material. Strouth II, 755 S.W.2d at 828. And the evidence of suspects other than Strouth and Dicks was already known to Strouth's attorney at the time of trial and was too vague and unsupported to be of use. Strouth III, 1997 WL 90636, at *8. When considered in tandem with the strong evidence of Strouth's guilt and the strong aggravating circumstanceslitting the throat of an unconscious seventy-year-old *608 manthis evidence had little prospect of changing the outcome of Strouth's trial. See Montgomery v. Bobby, 654 F.3d 668, 679-80 & n. 4 (6th Cir.2011) (en banc).

H.
Strouth argues his death sentence runs afoul of the Eighth (and Fourteenth) Amendment because no state court ever found beyond a reasonable doubt that he killed, attempted to kill or intended to kill Keegan. See Enmund v. Florida, 458 U.S. 782, 801, 102 S.Ct. 3368, 73 L.Ed.2d 1140 (1982). The problem is that the Court of Criminal Appeals explicitly held that Strouth's involvement in Keegan's murder satisfied the Enmund criteria. See Strouth II, 755 S.W.2d at 829. That is all the Constitution requires. Cabana v. Bullock, 474 U.S. 376, 386-87, 106 S.Ct. 689, 88 L.Ed.2d 704 (1986), abrogated on other grounds by Pope v. Illinois, 481 U.S. 497, 503 n. 7, 107 S.Ct. 1918, 95 L.Ed.2d 439 (1987).
Strouth resists this conclusion on two grounds. First, he takes issue with the failure of the Court of Criminal Appeals to discuss certain evidence Strouth considers favorable to his cause. But Enmund merely forbids the imposition of a death sentence on a defendant without a court making the necessary finding of personal involvement in the murder or intent to kill; it does not obligate a state court to discuss the evidence before it in any particular way. See Cabana, 474 U.S. at 386-88, 106 S.Ct. 689. Second, Strouth argues the state court must make the Enmund finding beyond a reasonable doubt. But the Supreme Court has never said the Enmund finding must be made beyond a reasonable doubt. If anything, the "considerable freedom" a State retains in "structur[ing] its capital sentencing system as it sees fit" suggests the Constitution requires no particular standard of proof. Id. at 386-87, 106 S.Ct. 689. At the least, that conclusion reasonably applies Supreme Court precedent.

I.
Strouth argues the guilt-phase jury instructions implied the jury could convict him if it had "a moral certainty," as opposed to certainty beyond a reasonable doubt, he committed the crime. Br. at 160. This claim is procedurally defaulted. Strouth sought to raise it in his second state collateral-review proceeding, but the Court of Criminal Appeals deemed it "waived for failure of appellant's counsel to raise this issue in a prior proceeding." Strouth III, 1997 WL 90636, at *10. Strouth makes no attempt to demonstrate cause for, and prejudice from, this procedural default, forfeiting the claim. He does argue that denying him review would amount to a fundamental miscarriage of justice, entitling him to review of an otherwise defaulted claim, but he points to no evidence that comes remotely close to establishing that this is the "extraordinary case" where "a constitutional violation has probably resulted in the conviction of one who is actually innocent." Murray v. Carrier, 477 U.S. 478, 496, 106 S.Ct. 2639, 91 L.Ed.2d 397 (1986). Even if it were not defaulted, the claim is transparently meritless. The trial court instructed the jury that "all elements of the offenses and any and all crimes required to be proved by the State must be proved beyond a reasonable doubt." Strouth App'x at 1392. That is a required instruction, not an improper one.

J.
Strouth argues that the prosecution, during the guilt-phase closing argument, improperly commented on Strouth's decision not to testify when it told the jury that there was no eyewitness testimony *609 about the murder because the victim was dead. This argument is procedurally defaulted because Strouth failed to present it to the Tennessee courts. See Pudelski v. Wilson, 576 F.3d 595, 605 (6th Cir.2009). Strouth argued in state court that during voir dire the prosecution improperly commented on his right to remain silent, but he said nothing about closing argument. Strouth I, 620 S.W.2d at 471-72. Once more, even if it were not defaulted, the claim lacks merit. The prosecution's discussion of the lack of eyewitnesses to the crime was not a convoluted attempt to call attention to Strouth's decision not to testify; it was an effort to respond to a weakness in the State's casethat no one saw Strouth kill Keegan. The Constitution does not prohibit this comment.

IV.
For these reasons, we affirm.
