BOGGS, J., delivered the opinion of the court, in which BATCHELDER, C.J., joined. GILMAN, J. (pp. 527-30), delivered a separate concurring opinion.
OPINION BOGGS, Circuit Judge.Steven Smith is an Ohio inmate sentenced to death for raping and murdering a six-month-old baby. We affirm the district court’s denial of a writ of habeas corpus.
I. Background
On September 28,1998, Smith was living with his girlfriend, Keysha Frye, and her two young daughters, two-year-old Ashley and six-month-old Autumn. That evening, Smith drank three beers while he, Frye, and the children visited a friend. On the way home, Smith bought a twelve-pack of beer and drank one in the car. Once back at Frye’s apartment, Smith and Frye put the children to bed, then watched television and had sex. Frye went to bed around 11:00 p.m., but Smith stayed up drinking.
At approximately 3:22 a.m., Smith woke Frye by placing Autumn’s naked body next to her. Frye realized that Autumn was not breathing and accused Smith of killing her; Smith threw an alarm clock and said that she was not dead. Frye quickly took Autumn’s body and Ashley to a neighbor’s apartment, screaming that Smith had killed her baby. Smith followed, exclaiming that he “didn’t do anything” and asking “why was she fucking lying,” but the neighbor did not let him in. A short while later, another neighbor observed Smith throw a trash bag in the dumpster and heard Smith say that he did not do anything and that he was leaving. This neighbor convinced Smith not to leave.
When the police arrived, they saw no signs of forcible entry in Frye’s apartment, and they found the television on and extremely loud. They discovered Autumn’s pink baby sleeper under the coffee table and Smith’s cutoffs and jeans near the couch. They also found whitish-colored material, later determined to be pieces of shredded diaper, scattered on the floor in the same area, and piles of Autumn’s hair were found on the coffee table. The police also retrieved a garbage bag from the outside trash dumpster that contained a *521torn baby diaper, Smith’s t-shirt, and ten empty beer cans.
When approached by an officer, Smith preemptively exclaimed, “I didn’t do it, I didn’t do it”; he smelled of alcohol and swayed back and forth while speaking. At the police station, Smith told detectives that he had drunk four beers that night. He stated that he and Frye had gone to bed at midnight and that he was awakened by Frye, who was accusing him of killing Autumn. A month later, Smith changed his story, telling police that he had consumed nine beers, and that he awoke downstairs at 3:25 a.m. and, believing that something was wrong with Autumn, carried her upstairs. He also denied putting trash in the dumpster.
Smith was charged with aggravated murder for raping and killing a child under the age of thirteen. At trial, the coroner who performed the autopsy testified extensively, using autopsy photographs and slides. He explained that Autumn died from compression asphyxia and blunt trauma to the head. The injuries to her head and the abrasions on her forehead, cheek, and chin indicated that she was lying on her abdomen and that her face had been forced into a pillow. Contusions to her buttocks indicated that they were subject to pressure from the weight of another person. Other bruising and abrasions revealed that Autumn had resisted the attack. She also suffered subarachnoid and retinal hemorrhages consistent with shaken baby impact syndrome, indicating that she had been restrained, and she was missing hair from the back of her head, suggesting that the attacker had forcefully grasped it. Furthermore, her clitoris was red, her vagina was ten times the normal size for a baby her age, and there was a hemorrhage in her anus, all indicative of attempted penetration. Additionally, Autumn’s blood was found on two seat cushions and on her pink sleeper. No semen was found.
Smith offered the testimony of a board-certified forensic toxicologist to support his intoxication defense. The police tested Smith’s blood-alcohol level at 11:00 a.m. on September 29, approximately seven hours after he was arrested, as 0.123%. The toxicologist testified that, based on this result, Smith’s blood-alcohol level would have been at least 0.36% and possibly as high as 0.60% at 11:30 p.m. on September 28. Smith also offered evidence that he drank as many as fifteen beers that night, and that he was an alcoholic who drank heavily and frequently blacked out.
The jury found Smith guilty as charged and sentenced him to death. The Ohio Supreme Court affirmed Smith’s conviction and sentence on direct appeal, State v. Smith, 97 Ohio St.3d 367, 780 N.E.2d 221 (2002), and the Ohio Court of Appeals denied his petition for postconviction review. The district court denied Smith’s petition for a writ of habeas corpus. Smith appeals, having received a certificate of appealability on four claims: (1) that the prosecutor improperly commented on his failure to testify; (2) that the penalty-phase jury instructions were misleading; (3) that counsel was constitutionally ineffective for failing to object to the misleading penalty instructions and for not requesting clarifying instructions; and (4) that the trial court should have instructed the jury on the lesser included offense of involuntary manslaughter.
II. Standard of Review
When a state court has “adjudicated ... the merits” of a defendant’s claim, we may only grant a writ of habeas corpus if the state court decision “was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme *522Court,” or “was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.” 28 U.S.C. § 2254(d). An adjudication on the merits is contrary to clearly established Supreme Court law if, for example, the “state court applies a rule that contradicts the governing law set forth in [Supreme Court] cases.” Williams v. Taylor, 529 U.S. 362, 405-06, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). An adjudication on the merits unreasonably applies Supreme Court law if, for example, “the state court identifies the correct governing legal rule ... but unreasonably applies it to the facts of the particular state prisoner’s case.” Id. at 407, 120 S.Ct. 1495. The application must be “objectively unreasonable,” not merely incorrect. Id. at 409-10, 120 S.Ct. 1495. When a state court’s adjudication on the merits is either contrary to or an unreasonable application of clearly established Supreme Court precedent, we “must then resolve the claim without the deference AEDPA otherwise requires.” Panetti v. Quarterman, 551 U.S. 930, 953, 127 S.Ct. 2842, 168 L.Ed.2d 662 (2007).
III. Prosecutorial Misconduct
Smith’s first claim is that the prosecutor improperly commented on his failure to testify during the guilt phase by telling the jurors to ask themselves, “[d]id [Smith] claim accident, that he didn’t do this on purpose?” See Griffin v. California, 380 U.S. 609, 615, 85 S.Ct. 1229, 14 L.Ed.2d 106 (1965). This claim is procedurally defaulted: counsel failed to object to the comment at trial, and the state court enforced the procedural bar by reviewing the claim only for plain error. See Seymour v. Walker, 224 F.3d 542, 557 (6th Cir.2000).
Smith asserts that we should not enforce his default. But his claim that the state courts do not regularly enforce Ohio’s contemporaneous objection rule is “squarely foreclosed” by our precedent. Nields v. Bradshaw, 482 F.3d 442, 451 (6th Cir.2007) (holding that Ohio’s state courts have not “applied its contemporaneous objection rule unevenly and inconsistently” with regard to prosecutorial misconduct claims). And he cannot excuse his default through the ineffectiveness of counsel because he cannot show that counsel’s failure to object to this one comment — thereby drawing attention to it — was deficient. Lundgren v. Mitchell, 440 F.3d 754, 774-75 (6th Cir.2006) (“[A]ny single failure to object [to closing arguments] usually cannot be said to have been error.... [Defense counsel must so consistently fail to use objections, despite numerous and clear reasons for doing so, that counsel’s failure cannot reasonably have been said to have been part of a trial strategy or tactical choice.”).
IV. Misleading Jury Instructions
We address Smith’s second and third claims together because both relate to the penalty-phase jury instructions. Smith’s second claim is that the penalty instructions violated Caldwell v. Mississippi 472 U.S. 320, 105 S.Ct. 2633, 86 L.Ed.2d 231 (1985), because they “affirmatively misled [the jury] regarding its role in the sentencing process,” Romano v. Oklahoma, 512 U.S. 1, 9, 114 S.Ct. 2004, 129 L.Ed.2d 1 (1994). Under Ohio law, the jury must unanimously recommend the death penalty; thus, “a solitary juror may prevent” it. State v. Brooks, 75 Ohio St.3d 148, 661 N.E.2d 1030, 1042 (1996). Smith contends that the instructions wrongly suggested that the jury was required to reject the death penalty unanimously, rather than to choose it unanimously.
This claim is also procedurally defaulted. Counsel did not object to the *523instructions as given. Smith wrongly suggests that the state court did not enforce the procedural bar because it did not discuss this claim “in terms of ‘plain error.’ ” After reviewing the several jury-instruction claims that Smith had preserved for appeal, the court stated: “As for the remaining arguments regarding jury instructions, since Smith did not raise an objection, we apply a plain-error analysis”; it then rejected, inter alia, this claim. Thus, the court enforced the procedural bar, see Seymour, 224 F.3d at 557.
Smith’s third claim is that his counsel was ineffective for failing to object to the penalty instructions as misleading and for not requesting an additional instruction explicitly stating that a solitary juror could prevent the death penalty. See Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). Although the state court rejected this claim on the merits, we review it de novo because Smith also argues that it excuses the default of his second claim. See Girts v. Yanai, 501 F.3d 743, 753 (6th Cir.2007). (“[Cjounsel cannot be ineffective for a failure to raise an issue that lacks merit.”). The instructions stated: “You shall impose the death sentence only if all 12 of you unanimously find [that the death penalty is appropriate], You shall impose one of the life imprisonment verdicts if all 12 of you do not unanimously find [that the death penalty is appropriate]” (emphasis added). This unmistakably informed the jury that the death penalty must be endorsed by every juror, and thus that one juror could prevent it. Cf. Hartman v. Bagley, 492 F.3d 347, 362-65 (6th Cir.2007) (rejecting an identical claim about the instruction, “[I]f ... you cannot unanimously agree that the [death penalty is appropriate], ... you will then [impose a life sentence]”). No other aspect of the instructions or the verdict forms undermined this clarity.
Smith’s counsel was also not ineffective for failing to request an additional “solitary juror” instruction, to which Smith was entitled under Ohio law, Brooks, 661 N.E.2d at 1042. Even if Smith’s counsel was deficient for failing to request the additional instruction, Smith cannot show a reasonable probability that the instruction would have led to a different outcome: the instructions as given adequately informed the jury that a single juror could prevent the death penalty, and thus an additional instruction would not have told the jury anything it did not already know.
Y. Lesser-Included-Offense Instruction
Smith’s final claim is that the trial court erred in refusing to instruct the jury on involuntary manslaughter. In capital cases, Beck v. Alabama requires that the jury be instructed on a noncapital lesser-included offense if, and only if, “the evidence would permit a jury rationally to find [the defendant] guilty of the lesser offense and acquit him of the greater.” 447 U.S. 625, 635, 100 S.Ct. 2382, 65 L.Ed.2d 392 (1980) (internal quotation marks omitted). Beck explained that “when the evidence unquestionably establishes that the defendant is guilty of a serious, violent offense — but leaves some doubt with respect to an element that would justify conviction of a capital offense — the failure to give the jury the ‘third option’ of convicting of a lesser included offense would seem inevitably to enhance the risk of an unwarranted conviction.” Id. at 637, 100 S.Ct. 2382.
Under Ohio law, involuntary manslaughter is a lesser included offense of aggravated murder, distinguished by the lack of intent to kill. State v. Campbell, 69 Ohio St.3d 38, 630 N.E.2d 339, 349 (1994). Smith contends that the trial court should have instructed the jury on involuntary manslaughter because, while there *524was overwhelming evidence that Smith raped and killed Autumn, the evidence of his voluntary intoxication would allow a rational jury to reasonably doubt whether he intended to kill her. The state court denied this claim on the merits, carefully recounting Autumn’s injuries and concluding that no reasonable juror could have found that Smith did not intend to kill her, given the brutality and duration of the crime.
Smith contends that the state court’s decision is both contrary to and an unreasonable application of Beck. He argues that the decision is contrary to Beck because the court did not, in fact, determine whether a rational jury reasonably could have doubted his intent to kill; rather, he maintains that the court rejected his claim only because he did not provide evidence of a specific intent to molest Autumn and because the evidence was sufficient to support the verdict. This argument fails. The court noted that Smith had not provided any evidence of an intent only to molest rather than to kill. Also, Smith never admitted that he molested her. And, while the state court’s opinion is not ideal, it plainly did not review the verdict only for the sufficiency of the evidence: the court properly recited Beck’s rule, it relied on three cases that properly applied Beck, and its analysis is consistent with Beck. Smith has failed to rebut the “presumption that state courts know and follow the law,” Woodford v. Visciotti, 537 U.S. 19, 24, 123 S.Ct. 357, 154 L.Ed.2d 279 (2002) (per curiam).
Smith’s argument that the state court unreasonably applied Beck requires more analysis, but also fails.1 It is well established that a lesser-included-offense instruction is not required where the facts of a murder so strongly indicate intent to kill that the jury could not rationally have a reasonable doubt as to the defendant’s intent. See, e.g., Hopper v. Evans, 456 U.S. 605, 613, 102 S.Ct. 2049, 72 L.Ed.2d 367 (1982) (denying a Beck claim where the defendant’s testimony and evidence that he shot the victim in the back during an armed robbery “affirmatively negated any claim that he did not intend to kill the victim”); Campbell v. Coyle, 260 F.3d 531, 543-44 (6th Cir.2001) (holding that the defendant’s Beck claim failed because the number and location of the victim’s five stab wounds “compelled a reasonable jury to find that the [defendant] possessed the intent to kill,” despite evidence of a struggle); see also Slaughter v. Parker, 450 F.3d 224, 236-38 (6th Cir.2006) (rejecting a Beck claim in the alternative because the “facts [that the victim was bludgeoned in the head and stabbed five times] foreclose the conclusion that [the defendant] acted with any mental state other than intent”); Abdus-Samad v. Bell, 420 F.3d 614, 629 (6th Cir.2005) (rejecting a Beck claim in the alternative because “[t]he fact that [the defendant] shot the victim with a pistol five to six times makes it virtually impossible to find that the killing was accidental”).
This case law reflects the sensible view that, as a general matter, repeated violent conduct conclusively proves intent to kill. Autumn’s death reflects such conduct: for ten to thirty minutes, Smith violently raped a six-month-old baby, during which time the baby resisted the attack and Smith forcibly subdued her by forcing her *525face into a pillow, ripping out her hair, shaking her, and causing deadly blunt force trauma to her head. Compared to the overwhelming proof of intent from such directed and persistent brutality, Smith’s intoxication evidence, which was not connected to any testimony that he was too drunk to form any intent, does not allow a juror rationally to acquit him of aggravated murder. Cf. Palmer v. Bagley, 330 Fed.Appx. 92, 99-100 (6th Cir.2009) (concluding “that a jury could not rationally have found that [the defendant] lacked the specific intent to kill each victim” where both were shot twice in the head at close range, “execution-style,” despite the defendant’s evidence that he was severely intoxicated from alcohol and LSD, that there had been a struggle, and his testimony that he did not intend to kill the victims). Therefore, we cannot say the state court’s decision was unreasonable.
Smith’s case may be compared usefully with the cases cited in the previous two paragraphs. Smith’s fundamental claim is that a jury could reasonably make the leap from his obvious intoxication to the conclusion that he did not intend to kill Autumn Frye. And, it is certainly not physically or logically impossible that he did not harbor such an intent, because the ultimate fact of intent can only be inferred, rather than ever known.
However, what Smith seeks from a jury would be a leap of faith, not an inferential leap based on evidence. We note that Smith did not contend, through his own testimony or any other type of circumstantial evidence, that he intended only molestation, but not killing. His basic position was always that no molestation occurred.
In the cases cited above, it was equally true that it was not physically or logically impossible that there was no intent to kill. In Hopper, it was not impossible that a gunman firing a shot that struck the victim in the back intended only to frighten or wound. In Campbell, it was not physically impossible that an assailant in a struggle might strike five wounds in the chest while intending only to disable but, as Judge Gilman’s opinion there ably showed, a conclusion need not be impossible to be unreasonable. 260 F.3d at 543-44. Similarly, the wounds delivered in Slaughter and in Abdus-Samad could in principle have been inflicted by a flailing assailant intending only minatory action, but there was no evidence that this theoretically possible situation occurred, just as in our case there is no evidence from which a jury could reasonably draw the conclusion that Smith intended some outrage, but not killing. In particular, the evidence showed not only simple asphyxiation, which might in theory have been caused only by Smith’s weight pressing on the baby in the course of a rape. Instead, the evidence directly showed blunt trauma to the head and shaken baby impact syndrome, indicative of lethal force purposefully applied.
And even if the state court’s analysis under Beck were unreasonable, we would analyze Smith’s claim under de novo review, Panetti 551 U.S. at 953, 127 S.Ct. 2842, and reject it because his evidence of intoxication was insufficient as a matter of state law to negate intent to kill. A lesser-included-offense instruction is required only where “the facts of the case and the laws of the State warrant such an instruction.” Hill v. Black, 920 F.2d 249, 251 (5th Cir.1990) (emphasis added); cf. Hopkins v. Reeves, 524 U.S. 88, 95-99, 118 S.Ct. 1895, 141 L.Ed.2d 76 (1998) (holding that Beck requires instruction only on crimes that are lesser included offenses under state law); Spaziano v. Florida, 468 U.S. 447, 456-57, 104 S.Ct. 3154, 82 L.Ed.2d 340 (1984) (holding that a lesser-included-offense instruction was not re*526quired when the lesser offense’s state-law statute of limitations had run).
Under Montana v. Egelhoff, states may regulate when — or if — evidence of voluntary intoxication can negate specific intent. 518 U.S. 37, 56, 116 S.Ct. 2013, 135 L.Ed.2d 361 (1996). We agree with our apparently unanimous sister circuits that, given Egelhoff, Beck claims based on voluntary intoxication that negates intent will fail unless the evidence of intoxication satisfies the state law requirements for negating intent. See, e.g., Spears v. Mullin, 343 F.3d 1215, 1244-45 (10th Cir.2003) (applying Oklahoma’s rule that the defendant must be “so intoxicated that his mental abilities were overcome or that the intoxication prevented him from acting with malice”); Skipper v. Lee, 238 F.3d 414 (Table), 2000 WL 1853330, at *5 (4th Cir.2000) (applying North Carolina’s rule that the defendant must produce “substantial evidence which would support a conclusion by the judge that he was so intoxicated that he could not form a deliberate and premeditated intent to kill”); Goodwin v. Johnson, 132 F.3d 162, 191-92 (5th Cir.1997) (holding that “the laws of [Texas] foreclose our finding a Beck violation on the basis [of] evidence of [the defendant’s] voluntary intoxication” because Texas does not allow voluntary intoxication to negate intent); Clabourne v. Lewis, 64 F.3d 1373, 1379-81 (9th Cir.1995) (explaining that in evaluating Beck claims based on intoxication, the court must “first consider whether Arizona recognizes intoxication as a defense to the premeditation element of first-degree murder”).
At the time of Smith’s conviction, Ohio law allowed voluntary intoxication to “create a reasonable doubt as to” the defendant’s intent to kill “[o]nly where the defendant was so intoxicated as to be mentally unable to intend anything.”2 State v. Otte, 74 Ohio St.3d 555, 660 N.E.2d 711, 720 (1996). Thus, even belief in a claim (not made here) that Smith only intended rape, but not murder, would not justify the instruction. The state court rejected Smith’s request for a voluntary-intoxication instruction, concluding that the evidence demonstrated that he could “intend [some]thing” at the time of the murder. Smith’s claim that this holding was error was not certified for appeal, and the state court’s holding therefore forecloses his Beck claim: as a matter of state law, Smith’s intoxication evidence could not create a reasonable doubt as to his intent to kill.
Nonetheless, we note our agreement with the state court’s conclusion. As we explained above, the facts of the crime demonstrate that Smith could “intend [some]thing.” So do his actions immediately before and after the murder. Smith apparently was aware enough to: turn up the volume on the television to drown out Autumn’s cries; remove her baby sleeper and tear apart her diaper; carry her body upstairs to her mother; have conversations with the neighbors and the police, and deny responsibility for her death repeatedly; and clean up the evidence of the murder and throw it away. These are not the aimless and uncontrolled actions of an individual incapable of “intending] anything.” Cf. Otte, 660 N.E.2d at 720-21 (finding that the defendant was not “so intoxicated as to be mentally unable to intend anything” because, inter alia, he turned up the volume of the television to drown out the victims’ cries, he shot them *527in the head, and he left the crime scene); State v. Tillman, 2000 WL 1682, at *3 (Ohio App. Dec. 20, 1999) (rejecting a request for voluntary-intoxication instructions where the defendant was able to ride a bike and “complet[e] the physical acts necessary for his part in getting aboard and absconding with [the victim’s] vehicle,” and where the defendant’s assault of the victim indicated “the cognitive wherewithal to understand that the vehicle’s owner stood as an impediment to getting away with the crime”); State v. Adkins, 1997 WL 66763, at *3 (Ohio App. Feb.ll, 1997) (rejecting a request for voluntary-intoxication instructions because, although the defendant was too intoxicated to give a statement to police upon arrest, he had been able to drive a car, have a conversation, and retrieve a gun before the murder).
VI. Conclusion
We AFFIRM the district court’s denial of habeas relief.
. Because we reject Smith's claim on the merits, we need not decide whether harmless error review can apply to Beck claims. Compare Hogan v. Gibson, 197 F.3d 1297, 1312 n. 13 (10th Cir.1999) (holding that it does not); Cordova v. Lynaugh, 838 F.2d 764, 767 (5th Cir.1988) (same), overruled on other grounds as recognized by Vanderbilt v. Collins, 994 F.2d 189, 195 (5th Cir.1993), with Gerlaugh v. Stewart, 129 F.3d 1027, 1031 (9th Cir.1997) (applying Brecht's harmless error standard to a Beck claim).
. Effective October 2000, Ohio eliminated voluntary intoxication as a defense to specific intent. See Ohio Rev.Code § 2901.21(C) (“Voluntary intoxication may not be taken into consideration in determining the existence of a mental state that is an element of a criminal offense.’’).