The United States Court of Appeals for the Sixth Circuit granted a writ of habeas corpus to respondent Gary Bradford Cone after concluding that the “especially heinous, atrocious, or cruel” aggravating circumstance found by the jury at the *448sentencing phase of his trial was unconstitutionally vague, and that the Tennessee Supreme Court failed to cure any constitutional deficiencies on appeal. 359 F. 3d 785, 799 (2004). Because this result fails to accord to the state court the deference required by 28 U. S. C. § 2254(d), we grant the petition for certiorari and respondent’s motion to proceed in forma pauperis and reverse.
I
Respondent killed Shipley Todd, 93, and his wife Cleopatra, 79, on August 10,1980, in their home at the conclusion of a 2-day crime spree. The killings were accomplished in a brutal and callous fashion: The elderly victims were “repeatedly beaten about the head until they died,” State v. Cone, 665 S. W. 2d 87, 90-91 (Tenn. 1984), and their bodies were subsequently discovered “horribly mutilated and cruelly beaten,” id., at 90. A Tennessee jury convicted respondent of, inter alia, two counts of murder in the first degree and two counts of murder in the first degree in the perpetration of a burglary. At the conclusion of the penalty phase of respondent’s trial, the jury unanimously found four aggravating circumstances1 and concluded that they outweighed the mitigating evidence. Respondent was sentenced to death.
The Tennessee Supreme Court affirmed respondent’s convictions and sentence. Id., at 96. As relevant here, the court held that three of the aggravating circumstances found by the jury “were clearly shown by the evidence.” Id., at *44994.2 With respect to the jury’s finding that the murders were “especially heinous, atrocious, or cruel,” the court said:
“The jury also found that the murders in question were especially heinous, atrocious, or cruel in that they involved torture or depravity of mind as provided in [Tenn. Code Ann.] § 39—2—203(i)(5). The evidence abundantly established that both of the elderly victims had been brutally beaten to death by multiple crushing blows to the skulls. Blood was spattered throughout the house, and both victims apparently had attempted to resist, because numerous defensive wounds were found on their persons. The only excuse offered in the entire record for this unspeakably brutal conduct by the accused was that these elderly victims had at some point ceased to ‘cooperate’ with him in his ransacking of their home and in his effort to flee from arrest. As previously stated, it was stipulated by counsel for [respondent] that there was no issue of self-defense even remotely suggested. The deaths of the victims were not instantaneous, and obviously one had to be killed before the other. The terror, fright and horror that these elderly helpless citizens must have endured was certainly something that the jury could have taken into account in finding this aggravating circumstance.” Id., at 94-95.
Respondent twice sought relief from his conviction and sentence in collateral proceedings in state court, to no avail. In his second amended petition for postconviction relief, respondent raised 52 independent claims of constitutional *450error, including a contention that the “especially heinous, atrocious, or cruel” aggravating circumstance was unconstitutionally vague under the Eighth Amendment. The state trial court held each of respondent’s claims barred by Tenn. Code Ann. §40-30-111 (1990), which limited the grounds that may be raised on collateral review to those not waived or previously determined in previous proceedings. The trial court explained that respondent’s constitutional challenge to the “heinous, atrocious, or cruel” aggravating circumstance, along with many other claims, was “clearly [a] re-statemen[t] of previous grounds heretofore determined and denied by the Tennessee Supreme Court upon Direct Appeal or the Court of Criminal Appeals upon the First Petition.” Cone v. State, No. P-06874 (Tenn. Crim. Ct., Dec. 16, 1993), p. 6. The Tennessee Court of Criminal Appeals affirmed the denial of relief on all grounds. Cone v. State, 927 S. W. 2d 579, 582 (1995). The State Supreme Court denied respondent permission to appeal.
II
In 1997, respondent sought a writ of habeas corpus under 28 U. S. C. § 2254 in the United States District Court for the Western District of Tennessee, again asserting a multitude of claims. The District Court denied relief; it held respondent’s vagueness challenge to the “especially heinous, atrocious, or cruel” aggravating circumstance to be procedurally barred by respondent’s failure to raise it on direct appeal in state court. The Court of Appeals for the Sixth Circuit subsequently held that respondent was entitled to relief on another ground and did not consider respondent’s challenges to the aggravating circumstances found by the jury. Cone v. Bell, 243 F. 3d 961, 975 (2001). We reversed that judgment. Bell v. Cone, 535 U. S. 685, 702 (2002).
On remand, the same panel of the Sixth Circuit again granted respondent a writ of habeas corpus, this time with one judge dissenting, on the ground that the “especially hei*451nous, atrocious, or cruel” aggravator was unconstitutionally vague under the Eighth Amendment. The court first rejected petitioner’s argument that respondent proeedurally defaulted the claim in state court. Based on its understanding of state law, the court concluded that the State Supreme Court’s statutorily .mandated review of each death sentence, see Tenn. Code Ann. § 39-2-205(c)(1) (1982), necessarily included the consideration of constitutional deficiencies in the aggravating circumstances found by the jury and therefore that the issue was “fairly presented” to the state court, even if respondent did not raise it himself.3 359 F. 3d, at 791-793. Judge Norris dissented on this point. Id., at 806.
Turning to the merits, the Sixth Circuit held that the state court’s affirmance of respondent’s sentence in light of the “especially heinous, atrocious, or cruel” aggravating circumstance was “contrary to” the clearly established principles set forth in our decision in Godfrey v. Georgia, 446 U. S. 420 (1980). The Court of Appeals allowed that “[n]o Supreme Court case has addressed the precise language at issue,” 359 F. 3d, at 795, and that no “Supreme Court decisio[n] is ‘on all *452fours’ with the instruction in Cone’s case,”4 id., at 796, but nevertheless concluded, in light of Godfrey and the series of cases that followed it, Maynard v. Cartwright, 486 U. S. 356 (1988), Walton v. Arizona, 497 U. S. 639 (1990), and Shell v. Mississippi, 498 U. S. 1 (1990) (per curiam), that federal law dictated the conclusion that the State’s “especially heinous, atrocious, or cruel” aggravator was unconstitutionally vague.5 359 F. 3d, at 797. Lastly, the court rejected petitioner’s argument that the Tennessee Supreme Court cured any deficiency in the aggravating circumstance on direct appeal by reviewing the jury’s finding under the narrowed construction of the aggravator that it adopted in State v. Dicks, 615 S. W. 2d 126 (1981). 359 F. 3d, at 797.
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A federal court may grant a writ of habeas corpus based on a claim adjudicated by a state court if the state-court decision “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). A state court’s decision is “contrary to . . . clearly established Federal law” “if the state court applies a *453rule that contradicts the governing law set forth in our cases,” or “if the state court confronts facts that are materially indistinguishable from a relevant Supreme Court precedent and arrives at a result opposite to ours.” Williams v. Taylor, 529 U. S. 362, 405 (2000).
The law governing vagueness challenges to statutory aggravating circumstances was summarized aptly in Walton, supra, overruled on other grounds, Ring v. Arizona, 536 U. S. 584 (2002):
“When a federal court is asked to review a state court’s application of an individual statutory aggravating or mitigating circumstance in a particular case, it must first determine whether the statutory language defining the circumstance is itself too vague to provide any guidance to the sentencer. If so, then the federal court must attempt to determine whether the state courts have further defined the vague terms and, if they have done so, whether those definitions are constitutionally sufficient, i. e., whether they provide some guidance to the sentencer.” Walton, supra, at 654.
These principles were plain enough at the time the State Supreme Court decided respondent’s appeal. In Proffitt v. Florida, 428 U. S. 242 (1976), we upheld the aggravating circumstance that the murder was “ ‘especially heinous, atrocious, or cruel’ ” on the express ground that a narrowing construction had been adopted by that State’s Supreme Court. Id., at 255 (joint opinion of Stewart, Powell, and Stevens, JJ.). And, in Gregg v. Georgia, 428 U. S. 153 (1976), we refused to invalidate the aggravating circumstance that the murder was “‘outrageously or wantonly vile, horrible or inhuman in that it involved torture, depravity of mind, or an aggravated battery to the victim,’ ” because “there [was] no reason to assume that the Supreme Court of Georgia will adopt ... an open-ended construction” that is potentially applicable to any murder. Id., at 201 (joint opinion of *454Stewart, Powell, and Stevens, JJ.). See generally Lewis v. Jeffers, 497 U. S. 764, 774-777 (1990) (reviewing eases).
Indeed, in Godfrey, 446 U. S. 420, the case on which the Court of Appeals relied in declaring the aggravating circumstance to be unconstitutionally vague, the controlling plurality opinion followed precisely this procedure. Like the court below, the plurality looked first to the language of the aggravating circumstance found by the jury and concluded that there was “nothing in these few words, standing alone, that implies any inherent restraint on the arbitrary and capricious infliction of the death sentence.” Id., at 428. But the plurality did not stop there: It next evaluated whether the Georgia Supreme Court “applied a constitutional construction” of the aggravating circumstance on appeal. Id., at 432. Because the facts of the case did not resemble those in which the state court had previously applied a narrower construction of the aggravating circumstance and because the state court gave no explanation for its decision other than to say that the verdict was “ ‘factually substantiated,’ ” the plurality concluded that it did not. Id., at 432-433. As we have subsequently explained, this conclusion was the linchpin of the Court’s holding: “Had the Georgia Supreme Court applied a narrowing construction of the aggravator, we would have rejected the Eighth Amendment challenge to Godfrey’s death sentence, notwithstanding the failure to instruct the jury on that narrowing construction.” Lambrix v. Singletary, 520 U. S. 518, 531 (1997). See also Walton, supra, at 653-654; Cartwright, supra, at 363-365 (refusing to countenance the Oklahoma Court of Criminal Appeals’ affirmance of a death sentence based on a facially vague aggravating circumstance where that court had not adopted a narrowing construction of its aggravator when it affirmed the prisoner’s sentence).6
*455In this case, however, the Sixth Circuit rejected the possibility that the Tennessee Supreme Court cured any error in the jury instruction by applying a narrowing construction of the statutory “heinous, atrocious, or cruel” aggravator. The court asserted that the State Supreme Court “did not apply, or even mention, any narrowing interpretation or cite to [sic] Dicks,” the case in which the State Supreme Court had adopted a narrowing construction of the aggravating circumstance. 359 F. 3d, at 797. “Instead,” the court said, “the [state] court simply, but explicitly, satisfied itself that the labels ‘heinous, atrocious, or cruel/ without more, applied to [respondent’s] crime.” Ibid.
We do not think that a federal court can presume so lightly that a state court failed to apply its own law. As we have said before, § 2254(d) dictates a “ ‘highly deferential standard for evaluating state-court rulings, Lindh v. Murphy, 521 U. S. 320, 333, n. 7 (1997), which demands that state-court decisions be given the benefit of the doubt.” Woodford v. Visciotti, 537 U. S. 19, 24 (2002) (per curiam). To the extent that the Court of Appeals rested its decision on the state court’s failure to cite Dicks, it was mistaken. Federal courts are not free to presume that a state court did not comply with constitutional dictates on the basis of nothing more than a lack of citation. See Mitchell v. Esparza, 540 U. S. 12, 16 (2003) (per curiam); Early v. Packer, 537 U. S. 3, 8 (2002) (per curiam).
More importantly, however, we find no basis for the Court of Appeals’ statement that the state court “simply, but explicitly, satisfied itself that the labels ‘heinous, atrocious, or cruel/ without more, applied” to the murder. 359 F. 3d, at 797. The state court’s opinion does not disclaim application of that court’s established construction of the aggravating *456circumstance; the only thing that it states “explicitly” is that the evidence in this case supported the jury’s finding of the statutory aggravator. See Cone, 665 S. W. 2d, at 95 (stating that the aggravating circumstance was “indisputably established by the record”). As we explain below, the State Supreme Court had construed the aggravating circumstance narrowly and had followed that precedent numerous times; absent an affirmative indication to the contrary, we must presume that it did the same thing here. See Visciotti, supra, at 24 (stating the presumption that state courts “know and follow the law”); Lambrix, supra, at 532, n. 4; Walton, 497 U. S., at 653. That is especially true in a case such as this one, where the state court has recognized that its narrowing construction is constitutionally compelled and has affirmatively assumed the responsibility to ensure that the aggravating circumstance is applied constitutionally in each case. See State v. Pritchett, 621 S. W. 2d 127, 139, 140 (Tenn. 1981).
Even absent such a presumption in the state court’s favor, however, we would still.conclude in this case that the state court applied the narrower construction of the “heinous, atrocious, or cruel” aggravating circumstance. The State Supreme Court’s reasoning in this case closely tracked its rationale for affirming the death sentences in other eases in which it expressly applied a narrowed construction of the same “heinous, atrocious, or cruel” aggravator. Accord, Godfrey, supra, at 432 (holding that “[t]he circumstances of this case ... do not satisfy the criteria [for torture] laid out by the Georgia Supreme Court itself” in its cases construing the aggravating circumstance). The facts the court relied on to affirm the jury’s verdict — that the elderly victims attempted to resist, that their deaths were not instantaneous, that respondent’s actions toward them were “unspeakably brutal,” and that they endured “terror, fright and horror” before being killed, 665 S. W. 2d, at 95—match, almost exactly, the reasons the state court gave when it held the evidence in State v. Melson, 638 S. W. 2d 342, 367 (Tenn. *4571982), to be sufficient to satisfy the torture prong of the narrowed “heinous, atrocious, or cruel” aggravating circumstance. See also Pritchett, supra, at 139 (finding the evidence to be insufficient to satisfy a narrowed construction of the aggravator where the victim’s death was “instantaneous”); State v. Campbell, 664 S. W. 2d 281, 284 (Tenn. 1984) (holding that evidence of the aggravator was “overwhelming” where an elderly murder victim was beaten to death with a blunt object and his hands showed that he had attempted to defend himself). Similarly, the state court’s findings that respondent’s victims had been “brutally beaten to death by multiple crushing blows to the skulls,” that “[bjlood was spattered throughout the house,” and that the victims were helpless, 665 S. W. 2d, at 94-95, accord with the reasons that the state court had previously found sufficient to support findings of depravity of mind. See Melson, supra, at 367; State v. Groseclose, 615 S. W. 2d 142, 151 (Tenn. 1981); Strouth v. State, 999 S. W. 2d 759, 766 (Tenn. 1999). In sum, a review of the state court’s previous decisions interpreting and applying the narrowed construction of the “heinous, atrocious, or cruel” aggravator leaves little doubt that the State Supreme Court applied that same construction in respondent’s case.7
The only remaining question is whether the narrowing construction that the Tennessee Supreme Court applied was *458itself unconstitutionally vague. See Walton, supra, at 654; Godfrey, 446 U. S., at 428. It was not. In State v. Dicks, 615 S. W. 2d 126 (Tenn. 1981), the state court adopted the exact construction of the aggravator that we approved in Proffitt, 428 U. S., at 255: that the aggravator was “directed at 'the conscienceless or pitiless crime which is unnecessarily torturous to the victim,”’ Dicks, supra, at 132. See also Sochor v. Florida, 504 U. S. 527, 536 (1992). In light of Prof-fitt, we think this interpretation of the aggravator, standing alone, would be sufficient to overcome the claim that the aggravating circumstance applied by the state court was “contrary to” clearly established federal law under 28 U. S. C. § 2254(d)(1).
The State Supreme Court’s subsequent application of this aggravating circumstance, as construed in Dicks, stands as further proof that it could be applied meaningfully to narrow the class of death-eligible offenders. Later in the year that Dicks was decided, the court elaborated on the meaning of the aggravator:
“Although the Tennessee aggravating circumstances [sic] [that the murder was heinous, atrocious, or cruel] does not contain the phrase, 'an aggravated battery to the victim[,]’ it is clear that a constitutional construction of this aggravating circumstance requires evidence that the defendant inflicted torture on the victim before death or that [the] defendant committed acts evincing a depraved state of mind; that the depraved state of mind or the torture inflicted must meet the test of heinous, atrocious, or cruel.” Pritchett, 621 S. W. 2d, at 139 (citation omitted).
With respect to the meaning of “torture,” the court held that the aggravator was not satisfied where the victim dies instantly, ibid., but that it was where “the uncontradicted proof shows that [the victim] had defensive injuries to her arms and hands, proving that there was time for her to real*459ize what was happening, to feel fear, and to try to protect herself,” Melson, 638 S. W. 2d, at 367. Accord, Cartwright, 486 U. S., at 364-365 (approving the limitation of the “heinous, atrocious, or cruel” aggravating circumstance to killings in which the victim suffered “some kind of torture or serious physical abuse” prior to the murder). As to “depravity of mind,” the court held the fact that the defendant fired a second shotgun blast into a victim after he was dead to be insufficient as a matter of law, see Pritchett, supra, at 139 (explaining that the depravity in such an action falls short of that exhibited by the defendant in Godfrey, supra), but concluded that, “a killing wherein the victim is struck up to thirty times, causing an entire room to be covered with a spray of flying blood, and causing the victim’s brains to extrude through the gaping hole in her skull,” sufficed, Melson, supra, at 367.8 In light of these holdings, we are satisfied that the State’s aggravating circumstance, as construed by the Tennessee Supreme Court, ensured that there was a “principled basis” for distinguishing between those cases in which the death penalty was assessed and those cases in which it was not. Arave v. Creech, 507 U. S. 463, 474 (1993).
In sum, even assuming that the Court of Appeals was correct to conclude that the State’s statutory aggravating circumstance was facially vague, the court erred in presuming that the State Supreme Court failed to cure this vagueness by applying a narrowing construction on direct appeal. The state court did apply such a narrowing construction, and that *460construction satisfied constitutional demands by ensuring that respondent was not sentenced to death in an arbitrary or capricious manner. See Godfrey, supra, at 428. The state court’s affirmance of respondent’s sentence on this ground was therefore not “contrary to... clearly established Federal law,” 28 U. S. C. § 2254(d)(1), and the Court of Appeals was without power to issue a writ of habeas corpus. We reverse the judgment of the Sixth Circuit and remand the case for further proceedings consistént with this opinion.
It is so ordered.
The jury found the following aggravating circumstances: (1) respondent had been convicted of one or more felonies involving the use or threat of violence to a person, (2) the murders were “especially heinous, atrocious, or cruel in that they involved torture or depravity of mind,” (3) respondent committed the murders for the purpose of preventing a lawful arrest or prosecution, and (4) respondent knowingly created a risk of death to two or more persons, other than the victim murdered, during the murder. See State v. Cone, 665 S. W. 2d 87, 94-95 (Tenn. 1984).
The state court rejected the jury’s finding that respondent “ ‘knowingly created a great risk of death to two (2) or more persons, other than the victim murdered, during his act of murder,’ ” on the ground that the considerable threat respondent posed to others earlier in the day was not sufficiently close in time to the murders. Based on the strength of the other aggravating circumstances before the jury, the court held this error to be “harmless beyond a reasonable doubt.” Id., at 95.
Petitioner argues that the Sixth Circuit’s conclusion in this regard is in tension with the decisions of other Courts of Appeals, which have held that a petitioner must raise his constitutional claim in state court in order to preserve it, notwithstanding the existence of a mandatory-review statute. See Mu’min v. Pruett, 125 F. 3d 192, 197 (CA4 1997) (Virginia); Martinez-Villareal v. Lewis, 80 F. 3d 1301, 1306 (CA9 1996) (Arizona); Kornahrens v. Evatt, 66 F. 3d 1350, 1362 (CA4 1995) (South Carolina); Nave v. Delo, 62 F. 3d 1024, 1039 (CA8 1995) (Missouri); Julius v. Johnson, 840 F. 2d 1533, 1546 (CA11 1988) (Alabama). We find it unnecessary to express a view on this point. See 28 U. S. C. § 2254(b)(2) (an application for habeas corpus may be denied on the merits, notwithstanding a petitioner’s failure to exhaust in state court). We do emphasize that, as a general matter, the burden is on the petitioner to raise his federal claim in the state courts at a time when state procedural law permits its consideration on the merits, even if the state court could have identified and addressed the federal question without its having been raised. See Baldwin v. Reese, 541 U. S. 27, 30-32 (2004).
The jury was instructed with respect to this aggravated circumstance as follows:
“ ‘Heinous’ means extremely wicked or shockingly evil.
“ ‘Atrocious’ means outrageously wicked and vile.
“ ‘Cruel’ means designed to inflict a high degree of pain, utter indifference to, or enjoyment of, the suffering of others, pitiless.” 359 F. 3d, at 794.
The court recognized that these cases postdated the Tennessee Supreme Court’s 1984 decision on direct appeal, but, relying on Stringer v. Black, 503 U. S. 222, 225 (1992) (which held that Cartwright did not announce a “new rule” of constitutional law because its resolution was dictated by Godfrey), concluded that these later cases were “not only material, but controlling” and required the conclusion that Tennessee’s “heinous, atrocious, or cruel” aggravating circumstance was unconstitutionally vague on its face. 359 F. 3d, at 795. We assume, without deciding, that the Court of Appeals was correct in this conclusion.
In Ring v. Arizona, 536 U. S. 584 (2002), we held that the Sixth Amendment requires a jury, rather than a judge, to find the aggravating circumstance that renders a defendant death eligible. Id., at 609. Because *455Ring does not apply retroactively, Schriro v. Summerlin, 542 U. S. 348, 358 (2004), this case does not present the question whether an appellate court may, consistently with Ring, cure the finding of a vague aggravating circumstance by applying a narrower construction.
We find additional support for this conclusion in the fact that respondent’s argument to the State Supreme Court relied squarely on a case in which that court had expressly formulated its narrowing construction of the aggravating circumstance and had applied that construction to the benefit of the defendant. See Brief for Appellant in No. 02C019403CR00052 (Sup. Ct. Tenn. 1983), p. 20 (arguing, based on State v. Pritchett, 621 S. W. 2d 127 (Tenn. 1981), that “the State did not show ... that the victims suffered”). Likewise, the two cases the State relied upon in response to respondent’s argument also expressly applied a narrowing construction of the “heinous, atrocious, or cruel” aggravator. See Brief for Appellee in No. 02C019403CR00052 (Sup. Ct. Tenn. 1983), p. 34 (citing Pritchett, supra, and State v. Melson, 638 S. W. 2d 342, 367 (Tenn. 1982)).
See also State v. Groseclose, 615 S. W. 2d 142, 151 (Tenn. 1981) (holding that raping and stabbing a victim, before killing her by locking her in a car trunk in the summer, satisfied the “heinous, atrocious, or cruel” aggravating circumstance); Strouth v. State, 999 S. W. 2d 759, 766 (Tenn. 1999) (quoting the State Supreme Court’s 1981 opinion denying rehearing, which held that cutting the throat of a victim already rendered unconscious demonstrated “depravity of mind” in that it was “cold-blooded, intentional, conscienceless and pitiless”); State v. Dicks, 615 S. W. 2d 126, 132 (Tenn. 1981) (affirming the jury’s application of the “heinous, atrocious, or cruel” aggravator to the same crime).