Opinion of the Court tain. 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 con Opinion of the Court strued 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 Opinion of the Court 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. Opinion of the Court 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 mur Opinion of the Court der, 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 ex |