Opinion

JUSTICE O'CONNOR delivered the opinion of the Court.

The question in this case is whether the Supreme Court of Arizona has cured petitioner's death sentence of vagueness error.

I

On August 25, 1973, Bernard Crummett had the misfortune to meet Rebecca Corella in a Tucson, Arizona, bar. Crummett left the bar with Corella and, in the parking lot, met petitioner, who had been waiting for Corella with his girlfriend, Faith Erwin. Corella agreed to perform an act of prostitution with Crummett, and petitioner drove the group to Corella's hotel. There, Corella communicated to petitioner that Crummett was "loaded," and petitioner in turn whispered to Erwin that he intended to rob Crummett.

After Corella and Crummett concluded their encounter at the hotel, the group again went for a drive, this time to a deserted area outside Tucson, where, Crummett believed, Corella would perform another act of prostitution. Petitioner stopped the car and got out. He first struck Crummett to the ground and next threw several large rocks at Crummett's head. Crummett's watch and wallet were taken by Corella, petitioner, or both, and these two then drove away with Erwin. Either petitioner or Corella was driving, and whoever it was drove the car over Crummett twice. Crummett suffered injuries to his head and trunk, and died.

The State of Arizona charged petitioner with robbery and first degree murder. Erwin testified at the jury trial that petitioner drove the car over Crummett, but admitted that she had been intoxicated by heroin at the time. A defense witness stated that Erwin previously had identified Corella as the driver. Neither Corella nor petitioner took the stand, although the prosecution did introduce a postarrest statement by petitioner in which he acknowledged robbing Crummett but claimed that Corella was the driver. There was medical testimony that a car had crushed Crummett's head, killing him, and that the injuries to his trunk, also vehicular, took place at least 30 seconds later.

Petitioner was convicted of both robbery and first degree murder. The jury was instructed as to the elements of felony murder as well as premeditated murder; the murder conviction was returned by a general verdict. Judge Roylston held the penalty hearing required by Ariz. Rev. Stat. Ann. § 13-703 (1989), then codified as § 13-454, and sentenced petitioner to death for the murder and 15-20 years' imprisonment for the robbery. The judge found two statutory aggravating factors: that petitioner had a prior felony conviction involving the use or threat of violence on another person, § 13-703(F)(2) (an armed kidnaping), and that petitioner "committed the offense in an especially heinous, cruel or depraved manner," § 13-703(F)(6) «F)(6) factor). Specifically, Judge Roylston's written order stated that "the Defendant did commit the offense in an especially heinous and cruel manner." App. 44. There was no explicit finding about the identity of the driver of the vehicle.

Petitioner unsuccessfully sought postconviction relief in the trial court, attaching two affidavits by persons who claimed to have been told by Corella that she, not petitioner, drove the car over Crummett. The Supreme Court of Arizona affirmed the sentence, conviction, and denial of postconviction relief. State v. Richmond, 114 Ariz. 186, 560 P. 2d 41 (1976). Although the opinion is ambiguous on this point, it appears that the court did not reach petitioner's vagueness challenge to the "especially heinous, cruel or depraved" factor because his death sentence was supported by another valid aggravating factor and no statutory mitigating factors applied. Id., at 196-197, 560 P. 2d, at 51-52. We denied certiorari. 433 U. S. 915 (1977). Federal habeas corpus proceedings ensued, as a result of which petitioner's conviction was found valid but his sentence invalid because the sentencing judge had been constrained to consider a limited set of mitigating factors. Richmond v. Cardwell, 450 F. Supp. 519 (Ariz. 1978). Soon thereafter, the Supreme Court of Arizona held the Arizona death penalty statute unconstitutional insofar as it limited defendants to statutory mitigating factors, State v. Watson, 120 Ariz. 441, 444-445, 586 P. 2d 1253, 1256-1257 (1978), and vacated every pending Arizona death sentence, see Brief for Respondents 5.

Petitioner's resentencing took place in March 1980. At the hearing, one defense witness testified that Erwin had identified Corella as the driver, while another stated that Corella had admitted the same. The defense also produced evidence of petitioner's rehabilitation in prison and of the effect his execution would have on his family. Judge Roylston again sentenced petitioner to death, this time finding three statutory aggravating circumstances: under Ariz. Rev. Stat. Ann. § 13-703(F)(2) (prior violent felony) and § 13703(F)(6) ("especially heinous, cruel or depraved" offense), as before, and also under § 13-703(F)(1) (prior felony meriting life imprisonment), for a murder charge of which petitioner had been convicted after the first sentencing even though the murder predated Crummett's. Once again, the judge found that "the Defendant did commit the offense in this case in an especially heinous and cruel manner," App. 74, but did not explicitly find that petitioner was the driver. The findings as to mitigation were, among others, that "Rebecca Corella was involved in the offense but was never charged with any crime"; that "Faith [E]rwin was involved in the offense but was never charged with any crime"; that "the jury was instructed both on the matters relating to the felony murder rule, as well as matters relating to premeditated murder"; and that "the Defendant's family ... will suffer considerable grief as a result of any death penalty that might be imposed." Id., at 75. The judge was unable to make a definitive finding as to rehabilitation and concluded that "there are no mitigating circumstances sufficiently substantial to call for leniency." Id., at 76.

A divided Supreme Court of Arizona affirmed, with each of the five justices joining one of three opinions. State v. Richmond, 136 Ariz. 312, 666 P. 2d 57 (1983) (Richmond II). Chief Justice Holohan wrote the principal opinion for himself and for Justice Hays, rejecting various challenges to petitioner's sentence, including a challenge to the (F)(6) factor. He reasoned that petitioner's offense was "heinous" and "depraved" (but not "cruel") and that this factor was not unconstitutionally vague:

"In [State v. Gretzler, 135 Ariz. 42, 659 P. 2d 1, cert. denied, 461 U. S. 971 (1983)], we discussed factors which lead to a finding of heinousness or depravity. One factor is the infliction of gratuitous violence on the victim; another related factor is the needless mutilation of the victim. Here the victim was already unconscious and bleeding when he was run over not once, but twice, each time from a different direction. The evidence indicates that the first run by the vehicle was over the victim's head crushing his skull and killing him. The second run of the vehicle was over the body of the victim .... Again the fact that the victim in the instant case was run over twice and his skull was crushed, we find to be a ghastly mutilation of the victim." Id., at 319, 666 P. 2d, at 64.

The principal opinion then conducted an independent review of the sentence, concluding that "the mitigation offered by [petitioner] is not sufficiently substantial to outweigh the [three] aggravating circumstances." Id., at 321, 666 P. 2d, at 66.

Justice Cameron, joined by Vice Chief Justice Gordon, wrote a special concurrence. "I concur in the [principal opinion] except its finding that this crime was heinous and depraved, and I concur in the result." Id., at 324,666 P.2d, at 69. The concurring justices contended that petitioner committed neither "gratuitous violence" nor "needless mutilation" within the meaning of State v. Gretzler, 135 Ariz. 42, 659 P. 2d 1, cert. denied, 461 U. S. 971 (1983). Gratuitous violence would have obtained only if petitioner "knew or should have known that the victim was dead after the first pass of the car" -if he "inflicted any violence on the victim which he must have known was 'beyond the point necessary to kill.'" Richmond II, 136 Ariz., at 323, 666 P. 2d, at 68. Similarly, needless mutilation was interpreted to mean "distinct acts, apart from the killing, specifically performed to mutilate the victim's body." Ibid. But the concurrence agreed that a death sentence was appropriate for petitioner, even absent the (F)(6) factor.

Justice Feldman dissented. He argued that the murder was not "especially heinous, cruel or depraved" and that the mitigating evidence of petitioner's rehabilitation precluded a death sentence. Id., at 324-325, 666 P. 2d, at 69-70.

We denied certiorari. 464 U. S. 986 (1983). Petitioner filed a habeas corpus action in the United States District Court for the District of Arizona, challenging his sentence and conviction. The District Court denied relief, Richmond v. Ricketts, 640 F. Supp. 767 (1986), and the Ninth Circuit affirmed, 921 F.2d 933 (1990). As to the (F)(6) factor, the panel held that a valid narrowing construction of that factor had been imposed in Richmond II and, in the alternative, that petitioner's sentence could stand without that factor despite our decision in Clemons v. Mississippi, 494 U. S. 738 (1990). "Elimination of the challenged factor would still leave enough support for [petitioner's] sentence because the statute at issue here is not a 'weighing' statute." 921 F.2d, at 947. The opinion later was amended to omit that sentence, but the amended opinion still reasoned: "Under the statute at issue in Clemons, the invalidation of an aggravating circumstance necessarily renders any evidence of mitigation 'weightier' or more substantial in a relative sense; the same, however, cannot be said under the terms of the Arizona statute at issue here." 948 F.2d 1473, 1488-1489 (1992).

The Ninth Circuit denied rehearing en bane, with four judges dissenting. Id., at 1476. We granted certiorari, 503 U. S. 958 (1992), and now reverse.

II

Petitioner challenges his death sentence imposed at resentencing in 1980. He argues that the "especially heinous, cruel or depraved" aggravating factor specified by Ariz. Rev. Stat. Ann. § 13-703(F)(6) (1989), upon which the sentencing judge relied, was unconstitutionally vague, and that the Supreme Court of Arizona failed to cure this invalidity in Richmond II.

The relevant Eighth Amendment law is well defined.

First, a statutory aggravating factor is unconstitutionally vague if it fails to furnish principled guidance for the choice between death and a lesser penalty. See, e. g., Maynard v. Cartwright, 486 U. S. 356, 361-364 (1988); Godfrey v. Georgia, 446 U. S. 420, 427-433 (1980). Second, in a "weighing" State, where the aggravating and mitigating factors are balanced against each other, it is constitutional error for the sentencer to give weight to an unconstitutionally vague aggravating factor, even if other, valid aggravating factors obtain. See, e. g., Stringer v. Black, 503 U. S. 222, 229-232 (1992); Clemons v. Mississippi, supra, at 748-752. Third, a state appellate court may rely upon an adequate narrowing construction of the factor in curing this error. See Lewis v. Jeffers, 497 U. S. 764 (1990); Walton v. Arizona, 497 U. S. 639 (1990). Finally, in federal habeas corpus proceedings, the state court's application of the narrowing construction should be reviewed under the "rational factfinder" standard of Jackson v. Virginia, 443 U. S. 307 (1979). See Lewis v. Jeffers, supra, at 781.

Arizona's "especially heinous, cruel or depraved" factor was at issue in Walton v. Arizona, supra. As we explained, "there is no serious argument that [this factor] is not facially vague." 497 U. S., at 654. Respondents do not argue that the factor had been narrowed adequately prior to petitioner's resentencing. Thus it would have been error for Judge Roylston to give weight to the (F)(6) factor, if he indeed balanced the aggravating and mitigating factors in resentencing petitioner, and respondents now agree that the judge did engage in this weighing process. See Brief for Respondents 44 ("Arizona Is a Weighing State"). The Arizona sentencing statute provides:

"In determining whether to impose a sentence of death ... the court shall take into account the aggravating and mitigating circumstances included in ... this section and shall impose a sentence of death if the court finds one or more of the aggravating circumstances ... and that there are no mitigating circumstances sufficiently substantial to call for leniency." Ariz. Rev. Stat. Ann. § 13-703(E) (1989).

This provision governed petitioner's resentencing and remains unamended in relevant part. Read most naturally, it requires the sentencer to weigh aggravating and mitigating circumstances-to determine the relative "substan[ce]" of the two kinds of factors. And the provision has been construed thus by the Supreme Court of Arizona. See, e. g., State v. Brewer, 170 Ariz. 486, 504, 826 P. 2d 783, 801, cert. denied, post, p. 872; State v. Gretzler, 135 Ariz., at 54-55, 659 P. 2d, at 13-14; State v. Valencia, 132 Ariz. 248, 250, 645 P.2d 239, 241 (1982); State v. Brookover, 124 Ariz. 38, 42, 601 P. 2d 1322, 1326 (1979). Nor do respondents contend that the (F)(6) factor had no effect on the sentencing judge's calculus and therefore was harmless.

Rather, they point to State v. Gretzler, supra, which issued subsequent to the resentencing but prior to Richmond II, and which provided an adequate narrowing construction of the "especially heinous, cruel or depraved" factor. See Lewis v. Jeffers, supra, at 777-778 (holding that Gretzler definitions adequately narrowed (F)(6) factor); Walton v. Arizona, supra, at 652-655 (same). Respondents assert that the principal opinion in Richmond II properly applied the Gretzler construction of the (F)(6) factor, while the concurrence ignored the factor, and that both opinions reweighed. Petitioner argues that the principal opinion improperly applied Gretzler, and that the concurrence did not reweigh.

We agree with petitioner that the concurrence in Richmond II did not reweigh. Our prior cases do not specify the degree of clarity with which a state appellate court must reweigh in order to cure an otherwise invalid death sentence, see Clemons v. Mississippi, supra, at 750-752; cf. Sochor v. Florida, 504 U. S. 527, 540 (1992) (discussing clarity of state appellate court's harmless-error analysis); Stringer v. Black, 503 U. S., at 229-232 (same), and we need not do so here. At a minimum, we must determine that the state court actually reweighed. "[W]hen the sentencing body is told to weigh an invalid factor in its decision, a reviewing court may not assume it would have made no difference if the thumb had been removed from death's side of the scale," id., at 232, nor can a court "cure" the error without deciding, itself, that the valid aggravating factors are weightier than the mitigating factors. "[O]nly constitutional harmless-error analysis or reweighing at the trial or appellate level suffices to guarantee that the defendant received an individualized sentence." Ibid. Where the death sentence has been infected by a vague or otherwise constitutionally invalid aggravating factor, the state appellate court or some other state sentencer must actually perform a new sentencing calculus, if the sentence is to stand.

The concurring justices in Richmond II did not purport to perform such a calculus, or even mention the evidence in mitigation. Respondents suggest that we presume reweighing, both because the justices of the Supreme Court of Arizona have an obligation to reweigh as part of their "independent review" of death sentences, and because Justices Cameron and Gordon concurred in the portion of the principal opinion that articulated this obligation. Although there is some force to this suggestion, any presumption of reweighing is overcome by the language of the concurrence itself. After arguing that petitioner's offense did not satisfy the (F)(6) factor, the concurrence offered this brief explanation why a death sentence was justified nonetheless.

"The criminal record of this defendant, however, clearly places him above the norm of first degree murderers. He has been convicted of another first degree murder and a kidnapping, each arising in separate incidents. This history of serious violent crime justifies the imposition of the death penalty." Richmond II, 136 Ariz., at 323-324, 666 P. 2d, at 68-69.

The plain meaning of this passage is that petitioner's aggravated background provided a conclusive justification for the death penalty. The passage plainly evinces the sort of automatic affirmance rule proscribed in a "weighing" State-"a rule authorizing or requiring affirmance of a death sentence so long as there remains at least one valid aggravating circumstance." Clemons v. Mississippi, 494 U. S., at 751.

As to the two justices who joined the principal opinion in Richmond II, Chief Justice Holohan and Justice Hays, petitioner argues that these justices erred by relying upon the (F)(6) "especially heinous, cruel or depraved" factor. Specifically, petitioner contends that the justices refrained from determining that he drove the car over Crummett; that in any case the record before the Supreme Court of Arizona did not suffice to support such a determination; and that the (F)(6) factor would not apply even if he were the driver, unless he knew when he drove the car over Crummett the second time that Crummett was already dead. Respondents dispute each of these points, arguing that Chief Justice Holohan and Justice Hays did determine petitioner to be the driver; that the sentencing judge had made an implicit finding on this score; and that the (F)(6) factor was applicable to the driver, whether or not he knew Crummett to be dead. The parties do agree that a state appellate court can cure a death sentence of constitutional error even where only a minority of the court relies upon a particular aggravating factor, as in Richmond II, if such reliance is otherwise legitimate. See Brief for Respondents 8-33; Reply Brief for Petitioner 3. We assume without deciding that the parties are correct on this point. Instead, the dispute here is simply whether the justices who relied upon the (F)(6) factor in Richmond II ought to have done so.

Of course, the question to be decided by a federal court on petition for habeas corpus is not whether the state sentencer committed state-law error in relying upon an adequately narrowed aggravating factor. See Lewis v. Jeffers, 497 U. S., at 780. Rather, the federal, constitutional question is whether such reliance is "so arbitrary or capricious as to constitute an independent due process or Eighth Amendment violation." Ibid. Gretzler, the narrowing construction of Arizona's (F)(6) factor, reads as follows:

"[T]he statutory concepts of heinous and depraved involve a killer's vile state of mind at the time of the murder, as evidenced by the killer's actions. Our cases have suggested specific factors which lead to a finding of heinousness or depravity.

"[One such factor] is the infliction of gratuitous violence on the victim ....

"[Another] is the needless mutilation of the victim."

135 Ariz., at 51-52, 659 P. 2d, at 10-11.

A murderer who intentionally drives a car over his victim twice arguably commits "gratuitous violence" within the meaning of Gretzler, whether or not he knows that the victim is dead after the first pass. An Arizona sentencer would not commit constitutional error by relying on the (F)(6) factor in sentencing that murderer. Although it may be true that knowledge of the victim's condition is required as a matter of Arizona law, indeed Richmond II itself may now stand for that state-law proposition, "federal habeas corpus relief does not lie for errors of state law." Lewis v. Jeffers, supra, at 780. On the other hand, respondents do agree that, on the facts of this case, the Eighth Amendment would preclude the application of the (F)(6) factor to petitioner if he did not intentionally drive the car over Crummett. Tr. of Oral Arg. 38-39. Cf. Tison v. Arizona, 481 U. S. 137, 156-158 (1987) (conduct short of intentional killing may show culpable mental state that justifies death penalty).

But we need not decide whether the principal opinion in Richmond II remained within the constitutional boundaries of the (F)(6) factor. Respondents assume that at least a majority of the Supreme Court of Arizona needed to perform a proper reweighing and vote to affirm petitioner's death sentence if that court was to cure the sentence of the initial vagueness error. See Brief for Respondents 27, 49, n. 16. Thus, even assuming that the two justices who joined the principal opinion properly reweighed, their votes did not suffice to validate the death sentence. One more proper vote was needed, but there was none. As we have already explained, the concurring justices who also voted to affirm petitioner's sentence did not perform a curative reweighing, while the dissenter voted to reverse. Therefore petitioner's sentence is invalid, whether or not the principal opinion properly relied upon the "especially heinous, cruel or depraved" factor.

III

Petitioner's death sentence was tainted by Eighth Amendment error when the sentencing judge gave weight to an unconstitutionally vague aggravating factor. The Supreme Court of Arizona did not cure this error, because the two justices who concurred in affirming the sentence did not actually perform a new sentencing calculus. Thus the sentence, as it stands, violates the Eighth Amendment.

We reverse the judgment of the Court of Appeals and remand with instructions to return the case to the District Court to enter an order granting the petition for a writ of habeas corpus unless the State of Arizona within a reasonable period of time either corrects the constitutional error in petitioner's death sentence or vacates the sentence and imposes a lesser sentence consistent with law.

It is so ordered.