Willie Lee Richmond, who was sentenced to death upon conviction of first-degree murder in Arizona state court, appeals from the district court’s denial of his petition for habeas corpus. He contends that imposition of capital punishment will violate his rights under the sixth, eighth, and fourteenth amendments. We now affirm.

I

A

This case arises from Richmond’s conviction in 1974 for first-degree murder in the death of Bernard Crummett. On an August evening seventeen years ago, the victim met Rebecca Corella, a nude dancer, at the Bird Cage Bar in Tucson, Arizona. After leaving the bar, the pair met Richmond in the bar’s parking lot where Corella attempted to persuade Richmond to allow his fifteen-year-old girlfriend, Faith Erwin, to prostitute herself with Crummett. Richmond and Erwin refused, and after a brief conversation, Corella agreed to have sex with Crummett herself. Crummett thereupon produced a twenty-dollar bill, which Corella handed to Richmond and which Richmond palmed and surreptitiously exchanged for a ten. A brief argument ensued as Richmond and Corella insisted that Crummett had only given them ten dollars.

Crummett eventually yielded and agreed to pay more. As he reached into his wallet a second time, Corella observed what seemed a considerable amount of cash, and she communicated her observation to Richmond. All four individuals then proceeded in a borrowed station wagon to Corella’s motel-room apartment. There, just as Co-rella and Crummett emerged from the bedroom, Richmond whispered to Erwin his intention that they rob Crummett, explaining that they should not commit the crime in the apartment because Crummett might remember the surroundings.

The group then left the motel and with Richmond as their driver proceeded to the end of a road on the outskirts of Tucson. Richmond thereupon stopped the car, and either Richmond or Corella — the testimony conflicts — told Crummett to get out because the car had suffered a flat tire. Richmond then assaulted Crummett, beating him with his fists and knocking Crum-mett to the ground. As Crummett lay motionless, Richmond pelted him with rocks. Corella, meanwhile, grabbed Crum-mett’s wallet. According to Erwin, who admitted that she was vomiting and “coming down” from heroin during the incident, the following events then transpired:

Under cross-examination, Erwin stood by her contention that Richmond had been the driver at the time the car ran over Crum-mett. She admitted, however, that she was suffering greatly under the influence of her drug injections at the time and that she was lying back on the car seat with her eyes closed.

The police found Crummett’s body at five o’clock the following morning. The examining pathologist 'testified at trial that the body exhibited signs of three forms of extreme force. First, there were wounds and indentations in the head consistent with a contention that the victim had been pummeled with rocks. In conjunction with this observation, he noted that several bloodstained rocks were found in the immediate vicinity of the body. Second, he testified that the victim’s head had suffered severe trauma and “bursting” from a crush injury most probably attributable to an automobile tire. He identified this second injury as the probable cause of death. Third, he testified to the presence of a second crush injury along the trunk and the abdominal section. This too the pathologist attributed to an automobile tire, which impacted the body from the opposite direction at least thirty seconds after the fatal blow. He concluded, therefore, that the victim was twice run over — once while alive but presumably unconscious and a second time after death. A police detective also testified to the discovery of human blood and hair on the undercarriage of the recovered station wagon.

Shortly after the night of Crummett’s death, Richmond was arrested on two unrelated murder charges. As he awaited proceedings on those charges in jail, he was served with an arrest warrant for the murder of Crummett, and he agreed to waive his rights and make a statement at that time. Although he admitted to robbing and beating Crummett, he claimed that he was not the driver when Crummett was run over. In his statement, which was taped and played at trial, Richmond insisted:

At the conclusion of the evidentiary phase of the trial, the judge instructed the jury that Richmond could be convicted of first-degree murder upon either a finding of premeditation or a felony-murder theory:

Upon these and other instructions, the jury found Richmond guilty of first-degree murder on February 5, 1974.

B

After a separate hearing held before the trial judge alone, the court pronounced its sentence:

State v. Richmond, 114 Ariz. 186, 189 , 560 P.2d 41, 44 (1976), cert. denied, 433 U.S. 915 , 97 S.Ct. 2988 , 53 L.Ed.2d 1101 (1977).

Richmond petitioned in state court for post-conviction relief claiming the discovery of new exculpatory evidence. He presented an affidavit from Daniel McKinney, a former boyfriend of Corella, in which McKinney stated that Corella had admitted to being the driver when the car ran over Crummett. The state countered with a transcribed tape recording in which McKinney claimed that Richmond had threatened him in prison. The petition for relief was denied. On automatic appeal, the Arizona Supreme Court affirmed both the conviction and the sentence, holding inter alia that (1) Richmond’s case was properly submitted on a theory of felony murder, (2) post-conviction relief was properly denied, and (3) the Arizona death penalty statute was constitutional, both as written and as applied. See 114 Ariz. at 190-98 , 560 P.2d at 45-53 .

After the United States Supreme Court denied certiorari on direct appeal, Richmond petitioned for a writ of habeas corpus in the federal district court of Arizona. He argued that the Arizona statute unconstitutionally deprived him of the opportunity to present non-statutory mitigating circumstances before the judge at sentencing. The district court upheld Richmond’s conviction but ruled the Arizona statute unconstitutional under the eighth and fourteenth amendments for its failure to allow consideration of a convict’s character. Richmond v. Cardwell, 450 F.Supp. 519 (D.Ariz.1978). The court therefore vacated Richmond’s sentence.

At a second sentencing hearing in March 1980, the state trial court again found no mitigating circumstances sufficient to warrant leniency, and it resentenced Richmond to death. Once again, on mandatory appeal, the Arizona Supreme Court affirmed the sentence. State v. Richmond, 136 Ariz. 312 , 666 P.2d 57 , cert. denied, 464 U.S. 986 , 104 S.Ct. 435 , 78 L.Ed.2d 367 (1983). Independently reviewing the record, the state supreme court found that Richmond had actively participated in the robbery and had played an integral role in the events leading up to Crummett’s death. Although it acknowledged that the force of Richmond’s manual blows had not caused the death, the court held that circumstantial evidence supported Erwin’s testimony that Richmond had been the lethal driver. It found that the sentence was appropriate under these conditions. Again on direct review, the United States Supreme Court denied certiorari. 464 U.S. 986 , 104 S.Ct. 435 , 78 L.Ed.2d 367 (1983).

Richmond then pursued a second writ of habeas corpus in federal court. After a brief hearing, the district court denied the writ and dismissed the petition. Four days later, a panel of this court stayed Richmond’s execution and issued a certificate of probable cause to provide time for a full-fledged appeal. In due course, the court affirmed dismissal for failure to exhaust state remedies, but it remanded with instructions to allow amendment to permit the prosecution of any claims that had been properly exhausted. Richmond v. Ricketts, 730 F.2d 1318 (9th Cir.1984). Following such amendment, the district court again denied Richmond’s petition, and this court again reversed, remanding for a full review of the state record. Richmond v. Ricketts, 774 F.2d 957 (9th Cir.1985). After reviewing the full record, the district court denied Richmond’s petition for the third time in a thirty-five page opinion. Richmond v. Ricketts, 640 F.Supp. 767 (D.Ariz.1986).

Richmond now appears before this court with the assistance of counsel to appeal this most recent denial order. This court originally entertained oral argument in his appeal on September 18, 1987, but deferred submission pending the en banc decision of this circuit in Adamson v. Ricketts. See No. 84-2069 (9th Cir. Aug. 14, 1987) (en banc) (order scheduling oral argument for Oct. 20, 1987, in light of Ricketts v. Adamson, 483 U.S. 1 , 107 S.Ct. 2680 , 97 L.Ed.2d 1 (1987)). Adamson presented a similar challenge to the constitutionality of Arizona’s revised death penalty statute. A year later, in December 1988, the Adam-son court ruled the Arizona statute unconstitutional. 865 F.2d 1011 (9th Cir.1988) (en banc). Arizona petitioned the Supreme Court of the United States for review of that decision, and this court further deferred submission pending that outcome.

In the meantime, on direct review from the state’s highest court, the Supreme Court of the United States announced in Walton v. Arizona that the Arizona death penalty statute is not unconstitutional. — U.S. —, 110 S.Ct. 3047 , 111 L.Ed.2d 511 (1990), reh’g denied, — U.S. —, 111 S.Ct. 14 , 111 L.Ed.2d 828 (1990). In a companion case decided that same day, Lewis v. Jeffers, the Court restated and elaborated upon its Walton holding. — U.S. —, 110 S.Ct. 3092 , 111 L.Ed.2d 606 , reh’g denied, — U.S. —, 111 S.Ct. 14 , 111 L.Ed.2d 829 (1990). On the following day, the Court denied certiorari in Adamson. Lewis v. Adamson, — U.S. —, 110 S.Ct. 3287 , 111 L.Ed.2d 795 (1990), denying cert. to Adamson v. Ricketts, 865 F.2d 1011 (9th Cir.1988) (en banc).

In light of these developments, this court ordered the parties to file supplemental briefs, and on September 27, 1990, the court entertained a second oral argument to consider the effects of Walton, Jeffers, and other recent Supreme Court decisions on this appeal. The court thereafter took the entire appeal under submission for decision.

II

A

The district court had proper jurisdiction under 28 U.S.C. § 2241 . This court has proper jurisdiction under 28 U.S.C. § 2253 . We review the denial of a habeas corpus petition de novo. See Weygandt v. Ducharme, 774 F.2d 1491, 1492 (9th Cir.1985). However, under 28 U.S.C. § 2254 (d), the factual findings of state trial and appellate courts are presumed correct if fairly supported by the record. See Sumner v. Mata, 449 U.S. 539, 546-47 , 101 S.Ct. 764, 768-69 , 66 L.Ed.2d 722 (1981).

B

Richmond has presented four arguments: (1) that Arizona’s death penalty law is unconstitutional both on its face and as applied, (2) that the trial court never specifically found that he caused, intended to cause, or attempted to cause Crummett’s death and that imposition of the death penalty would therefore violate the rule of Enmund v. Florida, 458 U.S. 782 , 102 S.Ct. 3368 , 73 L.Ed.2d 1140 (1982), (3) that he was improperly denied an evidentiary hearing on his claim that Arizona’s administration of the death penalty is unconstitutionally discriminatory, and (4) that fulfillment of his sentence after so many years on death row would constitute cruel and unusual punishment. Respondent Arizona has challenged all four contentions and has further argued that Richmond’s petition constitutes an abuse of the writ. We address the state’s latter contention first and then address Richmond’s arguments sequentially.

Ill

In its 1978 judgment on Richmond’s first petition for habeas relief, the district court vacated Richmond’s sentence but affirmed his conviction. The State of Arizona argues that because Richmond failed to appeal the affirmance of his conviction at that time, it is abuse of the writ to challenge the conviction now. See 28 U.S.C. § 2244 (b); Rules Governing Section 2254 Cases, Rule 9(b). A prior panel of this court has already addressed this contention. See Richmond, 774 F.2d at 959-61 . We are bound to adopt its conclusions as the law of the case. See Handi Inv. Co. v. Mobil Oil Corp., 653 F.2d 391 , 392 (9th Cir.1981); see also 1B J. Moore, J. Lucas & T. Currier, Moore’s Federal Practice ¶ 0.404[1], at 119 (2d ed. 1988) (“If there is an appeal from the judgment entered after remand, the decision on the first appeal establishes the law of the case to be followed on the second.”).

Thus, to the extent that Richmond seeks to challenge his conviction on grounds that were available to him when he filed his first petition, we agree that he is barred from doing so now:

Richmond, 774 F.2d at 960 (emphasis in original). Whether termed abuse of the writ or res judicata, the reassertion of such claims is not permissible at this stage.

Richmond, however, has focused his attention in the current appeal on challenging the re-imposition of his sentence. This he certainly may do, and in so doing, he may challenge the death penalty on grounds that were available to him but that he did not raise when contesting his first sentence:

Id. at 961 (citing Sanders v. United States, 373 U.S. 1, 18 , 83 S.Ct. 1068, 1078 , 10 L.Ed.2d 148 (1963)). Richmond may also renew challenges to the death penalty that were raised in his first petition and decided against him by the district court:

Id. at 960. With respect to any of the proffered challenges to his sentence, therefore, “Richmond’s petition does not constitute an abuse of the writ.” Id. at 961.

IV

A

At the time of Richmond’s conviction in 1974, Arizona law defined first-degree murder in relevant part as follows: “A murder which is perpetrated by ... any ... kind of wilful, deliberate and premeditated killing, or which is committed ... in the perpetration of, or attempt to perpetrate ... robbery ... is murder of the first degree.” Ariz.Rev.Stat.Ann. § 13-452 (repealed 1978) (current version at § 13-1105). For those convicted of first-degree murder, the Arizona code provides a sentencing hearing independent of the trial. § 13-703(B). Here, the trial judge must choose without the assistance of a jury between the options of life imprisonment and capital punishment. § 13-703(A)-(B). For purposes of this determination, a special verdict is required regarding the existence or non-existence of any aggravating or mitigating factors. § 13-703(D). The statute puts the burden of establishing the existence of any aggravating factors on the prosecution and the burden of establishing the existence of any mitigating factors on the defense. § 13-703(C). The statute then channels the court’s discretion:

§ 13-703(E) (emphasis added).

Subsection F enumerates ten aggravating circumstances, including the following three:

§ 13-703(F). By the time of Richmond’s resentencing in 1980, subsection G of the statute had been revised to read as follows:

§ 13-703(G).

B

Richmond challenges the constitutionality of this revised sentencing scheme on four grounds. First, he contends that judicial determination of the existence or nonexistence of aggravating circumstances im-permissibly usurps the jury’s fact-finding function. Second, he claims that requiring the defense to establish the existence of any mitigating circumstances illegitimately shifts the burden of proof. Third, he argues that the Arizona statute creates an unconstitutional presumption that death is the proper sentence. Finally, he insists that imposing the death penalty upon finding that the killing was “especially heinous, cruel or depraved” is unconstitutionally vague.

The Supreme Court’s recent decision in Walton v. Arizona specifically addressed and rejected the first three contentions, and Richmond has not forcefully advanced these arguments since. With respect to the judicial determination of sentencing factors, the Court stated: “ ‘Any argument that the Constitution requires that a jury impose the sentence of death or make the findings prerequisite to imposition of such a sentence has been soundly rejected by prior decisions of this Court.’ ” Walton, 110 S.Ct. at 3054 (quoting Clemons v. Mississippi, — U.S. —, 110 S.Ct. 1441, 1446 , 108 L.Ed.2d 725 (1990)). Indeed, even before Walton , it was well settled that “ ‘the Sixth Amendment does not require that the specific findings authorizing the imposition of the sentence of death be made by the jury.’ ” Id. (quoting Hildwin v. Florida, 490 U.S. 638, 640-41 , 109 S.Ct. 2055, 2057 , 104 L.Ed.2d 728 (1989)); see generally id. at 3054-55 (Part II of the opinion). As the district court noted when it rejected this argument in Richmond’s first petition:

Richmond, 450 F.Supp. at 523 (quoting Proffitt v. Florida, 428 U.S. 242, 252 , 96 5.Ct. 2960, 2966, 49 L.Ed.2d 913 (1976)).

The Walton Court likewise rejected the contention that requiring the defendant to establish the existence of mitigating factors impermissibly shifts the burden of proof. Denying that the practice violates the eighth and fourteenth amendments, the Court ruled:

Walton, 110 S.Ct. at 3055 ; see generally id. at 3055-56 (Part III of the opinion).

Finally, the Walton Court also rejected the claim that the Arizona statute creates an impermissible presumption that death is the proper sentence for first-degree murder. Like Richmond, Walton had challenged the statute’s directive that a court “shall impose a sentence of death” if it finds one or more aggravating circumstances and no substantial mitigating circumstances. Ariz.Rev.Stat.Ann. § 13-703(E) (emphasis added). Walton had contended, as Richmond does here, that this provision violates the proscription against mandatory death sentences announced in Woodson v. North Carolina, 428 U.S. 280 , 96 S.Ct. 2978 , 49 L.Ed.2d 944 (1976). The Court disagreed, citing its recent decisions in Blystone v. Pennsylvania, — U.S. —, 110 S.Ct. 1078 , 108 L.Ed.2d 255 (1990), and Boyde v. California, — U.S. —, 110 S.Ct. 1190 , 108 L.Ed.2d 316 , reh’g denied, — U.S. —, 110 S.Ct. 1961 , 109 L.Ed.2d 322 (1990), both of which had upheld similarly worded capital punishment laws. The Court ruled that so long as the statute provides individualized sentencing and does not automatically impose death for certain categories of murder, it passes constitutional muster under Woodson. See generally Walton, 110 S.Ct. at 3056 (Part IV of the opinion).

In short, the Supreme Court has specifically rejected three of the constitutional arguments raised here, and it has done so in the context of reviewing the very same statute.

C

Richmond insists, however, that his fourth constitutional challenge to the statute survives Walton . Indeed, he contends that Walton itself renders his death sentence unconstitutional and that this court’s en banc decision in Adamson v. Ricketts mandates resentencing. See Adamson, 865 F.2d 1011 (9th Cir.1988) (en banc), cert. denied sub nom. Lewis v. Adamson, — U.S. —, 110 S.Ct. 3287 , 111 L.Ed.2d 795 (1990). We are not persuaded.

In Walton , another Arizona inmate who was convicted of first-degree murder and sentenced to death challenged his sentence on constitutional grounds. The Supreme Court denied all four of his claims and affirmed the sentence. Despite this result, Richmond contends that Walton’s fourth claim and the Court’s disposition of that claim bolster his petition.

In his fourth claim, Walton alleged that the aggravating circumstance found and relied upon by the sentencing judge— his commission of the crime “in an especially heinous, cruel or depraved manner” —was unconstitutionally vague. Ariz.Rev. Stat.Ann. § 13-703(F)(6); see 110 S.Ct. at 3056-57. The Supreme Court agreed that the relevant statutory provision was vague but did not agree that it was unconstitutional. In essence, the Court held that facial vagueness alone does not decide the question: one must look beyond the language of the suspect provision and consider the full circumstances attending its application. Safeguards built into the sentencing scheme through other provisions-— and even extra-statutory procedural safeguards — may preserve the scheme’s constitutional integrity. See generally Walton, 110 S.Ct. at 3056-58 (Part V of the opinion).

The Court found three such safeguards within Arizona law. First, the Arizona scheme provides for sentencing by a judge, not by a jury. That fact alone distinguished Walton from Maynard v. Cartwright, 486 U.S. 356 , 108 S.Ct. 1853 , 100 L.Ed.2d 372 (1988), and Godfrey v. Georgia, 446 U.S. 420 , 100 S.Ct. 1759 , 64 L.Ed.2d 398 (1980), two cases relied upon by Walton in which the Supreme Court had invalidated death sentences due to similarly vague statutory definitions of aggravating circumstances. Where a judge makes the sentencing findings there is less danger of impermissibly broad applications of statutory terms: “Trial judges are presumed to know the law and to apply it [correctly] in making their decisions.” Walton, 110 S.Ct. 3057 .

Second, the Court found, the Arizona Supreme Court had effectively salvaged the suspect provision by affording it a “limiting definition” in the course of reviewing the trial judge’s sentencing decision. What the state legislature had improvidently left out, the state supreme court properly inserted:

Id. at 3057-58 (quoting State v. Walton, 159 Ariz. 571, 586 , 769 P.2d 1017, 1032 (1989)) (emphasis added). By injecting this limiting definition into a sentencing process already restricted to judges, Arizona provided ample protection for Walton’s constitutional rights.

Id. at 3057 (emphasis added).

Third, the Court reasoned:

Id.

In his reliance on Walton, Richmond points out as an initial matter that the same aggravating circumstance at issue in that case was cited by the Arizona Supreme Court in its review of his death sentence. Richmond insists that the terms of this aggravating circumstance — “especially heinous, cruel or depraved” — are facially vague. He is undeniably correct; Walton held so explicitly. Richmond then argues, however, that whereas the Arizona Supreme Court cured this potential defect in Walton, it failed to do so in his case. The court, he maintains, applied no comparable “limiting construction” in its review of his sentence. This contention is empirically incorrect.

In reviewing Richmond’s sentence, the Arizona Supreme Court quite clearly did provide a limiting construction for the admittedly vague aggravating circumstance. In fact, if anything, the state court provided a more narrowly tailored and more obviously sufficient limiting construction in Richmond’s case than it did in Walton’s:

Richmond, 136 Ariz. 312, 319 , 666 P.2d 57, 64 (plurality opinion) (finding Crummett’s killing especially heinous and depraved but not especially cruel); compare id. with Walton, 159 Ariz. at 586-88 , 769 P.2d at 1032-34 .

As in Walton, the sentence in this case was (a) imposed by a trial judge presumably knowledgeable in the law, (b) thoroughly and independently reviewed by the Arizona Supreme Court, and (c) reimposed under a sufficiently limiting construction. Under a fair reading of Walton and the record alone, therefore, Richmond’s contentions must fail.

Richmond attempts to avoid this conclusion by challenging the legal accuracy of the Arizona Supreme Court’s limiting construction. He cites several state court decisions, most notably State v. Gretzler, 135 Ariz. 42 , 659 P.2d 1 (1983), for the proposition that the court applied a definition of the aggravating circumstance that is untenable under Arizona law. This court, however, is foreclosed from engaging in any such inquiry. A federal appellate court cannot challenge the Arizona Supreme Court on matters of Arizona law; in that realm, the authority of the state court remains supreme.

Both Walton and its companion case, Lewis v. Jeffers, — U.S. —, 110 S.Ct. 3092 , 111 L.Ed.2d 606 (1990), support this analysis. As Walton pointed out, the relevant focus for this court’s attention is not upon the language of the Arizona statute per se or even upon the sentencing decision of the state trial judge; rather, it is upon the constitutional legitimacy of Richmond’s sentence as that sentence stands today after review by and exhaustion of the state court process. See Walton, 110 S.Ct. at 3057-58 . The only question for this court is whether the final state result violates constitutional law so as to warrant granting a writ of habeas corpus. Walton requires this court to pay due deference to state judicial systems in the administration of their own criminal sanctions and to recognize both the competence and duty of state courts of general jurisdiction to enforce federal constitutional law.

Jeffers thoroughly reinforces the Walton rule. In Jeffers , the Supreme Court restated and reapplied the Walton holding to deny another Arizona prisoner’s challenge to the legitimacy of his death sentence. Because Jeffers was before the Court on collateral review, the Court concluded that even greater deference was owed to the state system than the Court had urged in Walton, which it had heard on direct review. The Court never reached the merits of Jeffers’s constitutional claims, and it certainly never approached any questions of state law; rather, the Court reached its decision upon formulation of the appropriate standard of review. Writing for the Court, Justice O’Connor explained:

Jeffers, 110 S.Ct. at 3102 -03 (quoting Godfrey v. Georgia, 446 U.S. 420, 450 , 100 S.Ct. 1759, 1776 , 64 L.Ed.2d 398 (1980) (White, J., dissenting) and Jackson v. Virginia, 443 U.S. 307, 319 , 99 S.Ct. 2781, 2789 , 61 L.Ed.2d 560 , reh’g denied, 444 U.S. 890 , 100 S.Ct. 195 , 62 L.Ed.2d 126 (1979)) (emphasis in original).

In short, this court’s focus must not be on the underlying sentence but on whether the state system in both imposing and reviewing that sentence committed an independent constitutional violation. To vacate Richmond’s sentence, this court would have to find that there is no rational basis in law or fact for the state supreme court’s final evaluation that the circumstances warrant the sentence of death:

Id. at 3103 (emphasis added).

We therefore reject Richmond’s invitation to “conduct[] a de novo, case-by-case comparison of the facts” of various state court precedents. Id. at 3101. Like the Supreme Court in Walton, we “conclude that the definition given to the ‘especially cruel’ provision by the Arizona Supreme Court is constitutionally sufficient.” Walton, 110 S.Ct. at 3058 . Applying Jeffers , we further conclude that under that definition a rational factfinder could indeed have found Crummett’s murder heinous or depraved so as to warrant the penalty of death.

D

Even if Richmond were to prevail in his claim that the Arizona Supreme Court failed to provide a sufficiently limiting construction for the aggravating circumstance discussed above, however, his contentions would still lack merit. The Arizona Supreme Court rested its affirmance of his sentence upon a finding of not one, but three aggravating circumstances and an insufficient showing of mitigating circumstances. See Richmond, 136 Ariz. at 318-21 , 666 P.2d at 63-66 . The second aggravating factor relied upon was Richmond’s conviction for another murder six months after his initial conviction. Although this latter conviction postdated Richmond’s first, “[i]t is not disputed that the killing that was the basis of th[at] conviction occurred prior to the murder of Bernard Crummett.” Richmond, 640 F.Supp. at 780 ; see supra note '. In any event, both convictions were duly on record by the time of Richmond’s resentencing in 1980.

Furthermore, although the state supreme court explicitly found and addressed only these two aggravating circumstances, it held that “[t]he trial court correctly found three aggravating circumstances.” Richmond, 136 Ariz. at 320 , 666 P.2d at 65 . The third was an entirely separate prior conviction for kidnapping — statutorily relevant for death penalty purposes as an offense “involving the use or threat of violence on another person.” Ariz.Rev.Stat. Ann. § 13-703(F)(2). Arizona law explicitly provides that a single aggravating circumstance may suffice for imposition of the death penalty. See § 13-703(E).

Richmond does not contend, nor could he reasonably, that the statutory definitions of these two other factors are unconstitutionally vague. See § 13-703(F)(l)-(2). Rather, he sidesteps consideration of these additional factors by citing this circuit’s en banc decision in Adamson v. Ricketts for the proposition that invalidation of any one aggravating circumstance requires resentencing. See 865 F.2d at 1037 n. 42, 1038, 1039. We have just held that the aggravating circumstance to which Richmond refers is not invalid, but assuming for the sake of argument that it is, Richmond’s reliance on Adamson is not well taken.

The Supreme Court granted certiorari in Walton specifically because o/this circuit’s en banc holding in Adamson, and Walton reached the opposite conclusion regarding the Arizona statute’s constitutionality. Even if the portion of Adamson upon which Richmond relies survives Walton, it still does not support his claim. Contrary to the suggestion, Adamson did not hold that invalidation of one aggravating circumstance automatically requires remand for resentencing; rather, the court simply noted that it is the common practice of the Arizona Supreme Court to remand for re-sentencing when that court invalidates an aggravating circumstance. Id. There is no suggestion in Adamson that the United States Constitution requires remand when one aggravating factor is eliminated from the analysis if sufficient other aggravating factors remain.

The Supreme Court’s recent decision in Clemons v. Mississippi, — U.S. —, 110 S.Ct. 1441 , 108 L.Ed.2d 725 (1990), upon which Richmond also relies, is not to the contrary. In Clemons , a Mississippi inmate challenged the constitutionality of a death sentence imposed partially on the basis of a court’s finding that it had been an “especially heinous, atrocious or cruel” killing. Id., 110 S.Ct. at 1445. The Mississippi law in question permitted imposition of the death penalty upon a finding of only one aggravating circumstance so long as that aggravating circumstance outweighed all mitigating circumstances. Finding the state supreme court’s consideration of the “especially heinous” factor impermissibly vague, the Supreme Court remanded for resentencing.

The Court did not hold, however, that imposition of the death penalty on the basis of the single remaining aggravating factor would have been ipso facto unconstitutional. Rather, it implicitly recognized that reliance on a single aggravating factor can be constitutional. See id. at 1446, 1450-51. The Court remanded because once the vague factor was removed from the analysis, it was unclear from the Mississippi Supreme Court’s opinion whether the one remaining circumstance still outweighed all the mitigating evidence. See id. at 1449-51 (Parts III-IV of the opinion).

In this case, there is no similar doubt. Elimination of the challenged factor would still leave enough support for Richmond’s sentence because the statute at issue here is not a “weighing” statute. The Mississippi law that Clemons considered authorizes the death penalty if “ ‘there are insufficient mitigating circumstances ... to outweigh the aggravating circumstances.’ ” Id. at 1446 n. 2 (quoting Miss.Code Ann. § 99-19-101(3)(c) (Supp.1989)) (emphasis added). Arizona’s law authorizes the death penalty “if the court finds one or more of the [enumerated] aggravating circumstances ... and that there are no mitigating circumstances sufficiently substantial to call for leniency.” Ariz.Rev.Stat.Ann. § 13-703(E) (emphasis added). The difference is significant: a conclusion by the Arizona courts that there are no substantial mitigating circumstances is separate from and independent of any conclusion regarding the existence of aggravating circumstances. Invalidation of an aggravating circumstance does not mandate any reweighing or require resentenc-ing where the court has found that there is another aggravating circumstance and that the mitigating circumstances are insufficiently substantial to call for leniency.

V

Richmond next contends that because the trial court never specifically found that he caused, intended to cause, or attempted to cause Crummett’s death, imposition of the death penalty would violate the rule of Enmund v. Florida, 458 U.S. 782 , 102 S.Ct. 3368 , 73 L.Ed.2d 1140 (1982). The defendant in Enmund had been convicted of felony murder and sentenced to death for his involvement in the killing of two robbery victims, even though the record only suggested that he was the driver of the get-away car. In vacating En-mund’s sentence, the Supreme Court held that imposition of the death penalty violates the eighth and fourteenth amendments in the absence of a specific finding by the trier of fact that the defendant actually killed, attempted to kill, intended to kill, or contemplated that life would be taken:

Id. at 798 , 102 S.Ct. at 3377 ; see id. at 801 , 102 S.Ct. at 3378 .

Enmund , however, is clearly distinguishable from the present case. The jury that convicted Richmond received instructions on both premeditated and felony murder, and the record before us clearly provides sufficient evidence for a finding that Richmond expressly intended to participate in and to facilitate that murder. Moreover, the Supreme Court’s holding in Enmund was predicated upon the attenuated nature of the defendant’s responsibility for the deaths in that case. As the Supreme Court pointed out more recently in Tison v. Arizona, 481 U.S. 137 , 107 S.Ct. 1676 , 95 L.Ed.2d 127 , reh’g denied, 482 U.S. 921 , 107 S.Ct. 3201 , 96 L.Ed.2d 688 (1987), En-mund does not stand for the blanket proposition that capital punishment is unconstitutional in cases of felony murder:

481 U.S. at 157-58 , 107 S.Ct. at 1687-88 (footnote omitted).

Furthermore, in its independent review of the record in this case, the Arizona Supreme Court explicitly did consider En-mund, and it set forth findings sufficient to satisfy both that test and the Supreme Court’s later pronouncements in Tison :

Richmond, 136 Ariz. at 318 , 666 P.2d at 63 .

Nor does it matter that the Enmund finding was made by the state supreme court rather than by the original sentencing court:

Cabana v. Bullock, 474 U.S. 376, 386-87 , 106 S.Ct. 689, 696-97 , 88 L.Ed.2d 704 (1986) (footnote omitted). Accordingly, we conclude that the Arizona courts have predicated Richmond’s sentence upon a sufficient finding of criminal intent.

VI

As a black male of moderate means, Richmond next contends that the district court erred in denying his request for an evidentiary hearing upon his claim that Arizona’s administration of the death penalty is racially, sexually, and socio-economically discriminatory. We disagree. A habeas corpus petitioner is entitled to an evidentiary hearing both if he “alleges facts which, if proved, would entitle him to relief” and if he did not receive a full and fair evidentia-ry hearing on the issue in the state court. Townsend v. Sain, 372 U.S. 293, 312 , 83 S.Ct. 745, 756 , 9 L.Ed.2d 770 (1963); see id. at 312-19 , 83 S.Ct. at 756-60. The facts that Richmond has alleged, even if proven, would not entitle him to relief.

In support of his request for a hearing on this issue in the district court, Richmond made an extensive proffer of what he seeks to prove:

Brief for Appellant at 38-39 (citations omitted). This proffered evidence, however, is precisely the sort of generalized statistical evidence that was rejected as unactionable by the Supreme Court in McKleskey v. Kemp, 481 U.S. 279 , 107 S.Ct. 1756 , 95 L.Ed.2d 262 , reh’g denied, 482 U.S. 920 , 107 S.Ct. 3199 , 96 L.Ed.2d 686 (1987). Even if proven, the statistical disparities to which Richmond points would be insufficient to support an inference of purposeful discrimination in his own case. To require the district court to weigh this evidence would be to suggest that Richmond’s death sentence could conceivably be invalidated solely on the basis of his physical or social affinity to other defendants who are not now before this court but who may have suffered unconstitutional discrimination in their receipt of the same sentence. This we cannot do. To prevail in challenging his sentence under the equal protection clause, Richmond “must prove that the decision-makers in his case acted with discriminatory purpose.” McKleskey, 481 U.S. at 292, 107 S.Ct. at 1767 (emphasis in original). Richmond has alleged no facts to suggest that either the Arizoná Supreme Court, the state trial court, or the prosecutor’s office acted with prejudicial or discriminatory purpose in either seeking or imposing his sentence. The district court thus properly denied his request for an evidentiary hearing on this issue. See generally id. at 292-320, 107 S.Ct. at 1766-1782.

VII

Richmond’s final contention is that fulfillment of his sentence after sixteen years on death row would constitute cruel and unusual punishment in violation of the eighth and fourteenth amendments. We know of no decision by either the United States Supreme Court or this circuit that has held that the accumulation of time a defendant spends on death row during the prosecution of his appeals can accrue into an independent constitutional violation, and Richmond has cited no such decision.

On the other hand, the State of Arizona has directed the court’s attention to two relevant, though not controlling, precedents. In a decision affirmed two years later by the Tenth Circuit, the United States District Court for the District of Utah rejected a similar claim brought by a habeas corpus petitioner who had been on death row for ten years. Andrews v. Shulsen, 600 F.Supp. 408, 431 (D.Utah 1984), aff'd, 802 F.2d 1256 (10th Cir.1986), cert. denied, 485 U.S. 919 , 108 S.Ct. 1091 , 99 L.Ed.2d 253 , reh’g denied, 485 U.S. 1015 , 108 S.Ct. 1491 , 99 L.Ed.2d 718 (1988). The court reasoned that to accept the petitioner’s argument would be “a mockery of justice” given that the delay was attributa ble more to the petitioner’s actions than to the state’s. Id. Like Richmond, the petitioner in Andrews had sought “extensive and repeated review of [his] death sentence.” Id. Arizona also points to the well-known decision of the California Supreme Court in People v. Chessman, in which that court rejected the same claim by an eleven-year death-row inmate. 52 Cal.2d 467, 498 , 341 P.2d 679, 699 (1959), cert. denied, 361 U.S. 925 , 80 S.Ct. 296 , 4 L.Ed.2d 241 , reh’g denied, 361 U.S. 941 , 80 S.Ct. 383 , 4 L.Ed.2d 362 (1960). Finally, we note the decision of the United States Supreme Court in Harrison v. United States, 392 U.S. 219 , 221 n. 4, 88 S.Ct. 2008 , 2009 n. 4, 20 L.Ed.2d 1047 (1968), which the district court cited in its rejection of this claim and which held that an eight-year delay between an arrest and sentencing was not unconstitutional where the delay resulted from the need to assure careful review of an unusually complex case. See Richmond, 640 F.Supp. at 803 (citing Harrison).

Especially in light of the relative absence of contrary precedents, we believe that the reasoning of these cases is sound. A defendant must not be penalized for pursuing his constitutional rights, but he also should not be able to benefit from the ultimately unsuccessful pursuit of those rights. It would indeed be a mockery of justice if the delay incurred during the prosecution of claims that fail on the merits could itself accrue into a substantive claim to the very relief that had been sought and properly denied in the first place. If that were the law, death-row inmates would be able to avoid their sentences simply by delaying proceedings beyond some threshold amount of time, while other death-row inmates— less successful in their attempts to delay— would be forced to face their sentences. Such differential treatment would be far more “arbitrary and unfair” and “cruel and unusual” than the current system of fulfilling sentences when the last in the line of appeals fails on the merits. We thus decline to recognize Richmond’s lengthy incarceration on death row during the pend-ency of his appeals as substantively and independently violative of the Constitution.

VIII

For the foregoing reasons, we affirm the judgment of the district court and deny Richmond’s petition for a writ of habeas corpus.

AFFIRMED.

. On August 9, 1974, Richmond was convicted of first-degree murder on one of the two unrelated charges and sentenced to life imprisonment. “It is not disputed that the killing that was the basis of th[at] conviction occurred prior to the murder of Bernard Crummett.” Richmond v. Ricketts, 640 F.Supp. 767, 780 (D.Ariz. 1986). At the time of that earlier murder, "the death [penalty] had not yet become effective [in Arizona] so that the sentence of life imprisonment was the only possible sentence.” Id. Richmond was acquitted of the other murder. See id. . The Arizona death penalty statute was subsequently revised to cure this defect. See Ariz. Rev.Stat.Ann. § 13-703(G), as amended by 1979 Ariz.Sess.Laws ch. 144, § 1 (effective May 1, 1979). . See infra note 10. . Under the "total exhaustion rule” announced by the Supreme Court in Rose v. Lundy, 455 U.S. 509 , 102 S.Ct. 1198 , 71 L.Ed.2d 379 (1982), a federal court cannot adjudicate a habeas petition if it contains any unexhausted claims — even if it also contains exhausted claims. The remand order was intended to satisfy this rule. See 730 F.2d at 1318 . Upon amending his petition, Richmond continued to assert eighteen claims. See 774 F.2d at 959. . We have already had occasion to note Walton 's rejection of the first and third contentions. See Smith v. McCormick, 914 F.2d 1153, 1169-70 (9th Cir.1990). We also note in passing that Richmond's able and experienced counsel, Timothy K. Ford, is intimately familiar with the Walton case. Mr. Ford represented Jeffrey Alan Walton in his petition before the United States Supreme Court. This fact—in addition to the cases’ underlying similarity—may help to explain why several of the arguments raised here are identical to arguments decided by the Court in that case. See infra note 7 (noting the factual similarities between the two cases). . Since the Walton decision, Richmond has apparently conceded that the sixth amendment does not require jury factfinding at the sentencing phase in capital punishment cases, but he has stressed the alternative argument that the equal protection clause does require jury fact-finding at sentencing. Because Arizona law provides for jury factfinding in many similar circumstances, Richmond contends, it is arbitrary and irrational not to provide for it here. We find this argument unpersuasive. As the Supreme Court noted in Proffitt , there is indeed a rational reason for committing the factfinding function to the judge at the sentencing phase in capital punishment cases, and it probably promotes more evenhanded justice to do so. See Proffitt, 428 U.S. at 252 , 96 S.Ct. at 2966 . Moreover, the Court’s sixth amendment holding on this issue in Walton would make little sense if the broader, less specific terms of the equal protection clause could be read to require the opposite result. . The facts of the Walton case are strikingly similar in many respects to the facts of the present case. Walton, who also acted with the assistance of two friends, "went to a bar in Tucson, Arizona, ... intending to find and rob someone at random, steal his car, tie him up, and leave him in the desert.... In the bar’s parking lot, the trio encountered Thomas Powell, a young, off-duty Marine.” 110 S.Ct. at 3052. Forcing Powell to accompany them, the three commandeered his car and drove to a remote area on the outskirts of town. When they stopped, they forced Powell out of the car and had him lie face down on the ground near the car while they debated what to do with him_ Walton then took a .22 caliber derringer and marched Powell off into the desert. After walking a short distance, Walton forced Powell to lie down on the ground, placed his foot on Powell’s neck, and shot Powell once in the head. Walton later told [his two accompany ing friends] that he had shot Powell and that he had "never seen a man pee in his pants before." Id. Despite the similarities, the circumstances of Powell’s death were somewhat more gruesome than those of Crummett's: Powell’s body was found approximately a week later_ A medical examiner determined that Powell had been blinded and rendered unconscious by the shot hut was not immediately killed. Instead, Powell regained consciousness, apparently floundered about in the desert, and ultimately died from dehydration, starvation, and pneumonia approximately a day before his body was found. Id. . Walton's first three claims, which were also raised by Richmond, were the three claims discussed in Part IV-B above. First, Walton alleged that "every finding of fact underlying the sentencing decision must be made by a jury, not by a judge." 110 S.Ct. at 3054; compare Ariz. Rev.Stat.Ann. § 13-703(B). Second, he alleged that the Arizona statute unconstitutionally "imposes on defendants the burden of establishing, by a preponderance of the evidence, the existence of mitigating circumstances." 110 S.Ct. at 3055; compare Ariz.Rev.Stat.Ann. § 13-703(C). Third, he alleged that the Arizona statute "creates an unconstitutional presumption that death is the proper sentence" because it requires the death penalty "if one or more aggravating circumstances are found and mitigating circumstances are held insufficient to call for leniency." 110 S.Ct. at 3056; compare Ariz.Rev.Stat. Ann. § 13-703(E). The Supreme Court rejected all three of these claims as well as the fourth, which is discussed herein. . Richmond argues that only two of the five Justices of the Arizona Supreme Court concurred in this portion of the court's opinion. He is correct. Two other Justices voted to affirm the sentence but on other grounds. They explicitly rejected the argument that the killing had been especially heinous and depraved. See Richmond, 136 Ariz. at 322-24 , 666 P.2d at 67-69 (Cameron, J., concurring and Gordon, V.C.J., joining). The fifth Justice dissented altogether. See 136 Ariz. at 324-26 , 666 P.2d at 69-71 (Feld-man, J., dissenting). The fact that a majority of the court did not concur in this finding, however, does not deny that the Justices who did concur in it provided an adequate limiting construction. The relevant point is that members of the court who premised their votes on the challenged factor undertook the deliberations and analysis constitutionally required. More importantly, Richmond's observation is irrelevant in light of the fact that four Justices concurred in the finding of two other aggravating circumstances, either one of which could constitutionally have justified imposition of the death penalty. See infra Part IV-D. . See Richmond, 136 Ariz. at 317 , 666 P.2d at 62 (“[I]n each case where the death penalty is imposed, this court conducts an independent review of the record to assure a just result. We have reviewed the record in the instant case ..."); 136 Ariz. at 320 , 666 P.2d at 65 ("In death penalty cases, this court will conduct an independent examination of the record to determine for ourselves the presence or absence of aggravating and mitigating circumstances and the weight to give to each. We also independently determine the propriety of the sentence.’’). . The court also hinted at the possible applicability of a fourth aggravating circumstance: the defendant’s commission of the crime in expectation of pecuniary gain. See Ariz.Rev.Stat.Ann. § 13 — 703(F)(5); Richmond, 136 Ariz. at 320 , 666 P.2d at 65 . Although noting that the trial court had improperly analyzed this factor in reaching the conclusion that it did not apply, the Arizona Supreme Court declined to determine whether under a proper analysis it would apply. With respect to consideration of Richmond’s kidnapping conviction, the Arizona Supreme Court's majority opinion does not address it except to express general agreement with the trial court’s reliance upon it. The concurrence, which was endorsed by two Justices, is somewhat more explicit in its embrace of the lower court’s reliance on both the prior murder conviction and the prior kidnapping conviction. See Richmond, 136 Ariz. at 323-24 , 666 P.2d at 68-69 (Cameron, J., concurring and Gordon, V.C.J., joining). . See Walton, 110 S.Ct. at 3054 (“Because the United States Court of Appeals for the Ninth Circuit has held the Arizona death penalty statute to be unconstitutional for the reasons submitted by Walton in this case, see Adamson v. Ricketts, 865 F.2d 1011 (1988) (en banc), we granted certiorari.”); id. at 3059 (Scalia, J., concurring) (describing Adamson and Walton as "essentially identical” cases). . Interestingly, the Arizona Supreme Court conducted its Enmund analysis in this case before the United States Supreme Court narrowed the Enmund holding in Tison . The United States Supreme Court decided Enmund in 1982; the Arizona Supreme Court affirmed Richmond’s sentence in 1983; and the United States Supreme Court decided Tison in 1987. . Richmond actually alleged that fulfillment of his sentence after thirteen years on death row would constitute cruel and unusual punishment. Because he raised that claim in his opening brief, which was filed in 1987, we have added the past three years during which we deferred submission of his appeal. We note, however, that because this appeal properly concerns Richmond’s sentence only as of the date of its reim-position in 1980, the relevant period of his residency on death row is actually ten years.