William Andrews appeals from an order of the United States District Court for the District of Utah dismissing a habeas corpus petition challenging the constitutionality of his death sentence. See Andrews v. Skulsen, 600 F.Supp. 408 (D.Utah 1984) (Andrews IV). We affirm.
I.
BACKGROUND
The facts of this case, as reported in opinions of the Utah Supreme Court, are as follows:
“[Dale Pierre,] Andrews, and [Keith] Roberts were airmen stationed at Hill
*1259Air Force Base, Utah. Stanley Walker, Michelle Ansley, Carol Naisbitt, Cortney Naisbitt (son of Carol Naisbitt), and Orren W. Walker, Jr. (father of Stanley Walker) were tied up, made to lie on the floor, and forced to drink liquid Drano on the evening of April 22, 1974, in the basement of the Hi-Fi Shop in Ogden, Utah, by [Pierre] in company with Andrews, who aided [Pierre] by pouring the caustic substance into a plastic cup for accomplishment of these violent acts. [Pierre] and Andrews both had hand guns and [Pierre] finally shot all of the victims in the head with either a .25 caliber or .38 caliber handgun, which caused the deaths, within a brief period of time during that April evening, of Stanley Walker, Michelle Ansley (who had also been raped by [Pierre] just before he shot her) and Carol Naisbitt.
“[A]fter shooting [Orren Walker, Pierre] vehemently kicked a ball point pen into one of his ears and attempted to strangle him with a cord.”
State v. Pierre, 572 P.2d 1338, 1343-44 (Utah 1977) (footnote omitted), cert. denied, 439 U.S. 882, 99 S.Ct. 219, 58 L.Ed.2d 194 (1978).
“Evidence by witness Orren W. Walker, Jr. at the guilt phase revealed that [Andrews] asked Pierre in the basement of the Hi-Fi Shop, after Pierre had discharged his hand gun (not at that time shooting anyone), ‘What did you do that for, man’; that [Andrews] was nervous and upset; that when Walker made no movement after being told by Pierre to administer the Drano to Michelle Ansley, Stanley Walker, and Cortney Naisbitt, [Andrews] said to Walker, ‘Man, there is a gun at your head’; that either before or after the administration of the Drano to the victims [Andrews] said: T can’t do it, I’m scared’, though Walker stated he did not know to what this remark of [Andrews’] referred; and that Andrews, who left and returned to the basement on more than one occasion during the evening of April 22nd, was not observed firing any gun nor was he present when Michelle was raped and all the victims were shot.”
State v. Andrews, 574 P.2d 709, 709-10 (Utah 1977) (Andrews I), cert. denied, 439 U.S. 882, 99 S.Ct. 219, 58 L.Ed.2d 194 (1978).
“Evidence further established that Orren and Stanley Walker were robbed in an aggravated manner of personal property in their possession (equipment from the Hi-Fi Shop being taken from Stanley and a watch and wallet being taken from Orren) ... by [Pierre], Andrews, and Roberts. [Pierre] and Andrews were identified inside of said shop during the robbery and Roberts was identified walking in front of it.”
Pierre, 572 P.2d at 1343.
The three men were apprehended and tried together before a jury. Andrews and Pierre were found guilty on three counts of first degree murder and two counts of aggravated robbery. Roberts was convicted of aggravated robbery, but the jury was unable to reach a verdict on the murder charges. After a separate sentencing hearing, the same jury voted unanimously to impose the death penalty on Andrews and Pierre for each of the murder convictions. On November 27, 1974, the trial judge sentenced them to death before a firing squad. During the next six years, Andrews unsuccessfully challenged his conviction and sentence on direct appeal, see Andrews I, 574 P.2d 709, and in collateral state proceedings, see Andrews v. Morris, 607 P.2d 816 (Utah) (Andrews II), cert. denied, 449 U.S. 891, 101 S.Ct. 254, 66 L.Ed.2d 120 (1980).
In November 1980, Andrews filed this action for federal habeas corpus relief. The State responded by moving to dismiss his petition on the merits and on the basis of alleged procedural defaults in the state courts. While the federal proceedings were pending, the Utah Supreme Court decided State v. Wood, 648 P.2d 71 (Utah 1981) (per curiam), cert. denied, 459 U.S. 988, 103 S.Ct. 341, 74 L.Ed.2d 383 (1982), which raised the burden of persuasion in the sentencing phase of Utah capital cases. *1260The federal district court stayed further proceedings while Andrews again sought collateral state relief. The Utah Supreme Court declined to apply Wood retroactively and denied Andrews’ petition for relief. See Andrews v. Morris, 677 P.2d 81 (Utah 1983) (Andrews III).
The district court then ordered the parties to address all outstanding issues. In his second amended petition, Andrews claimed that: (1) Utah had denied him a fair and impartial jury trial; (2) the Utah capital punishment statute was unconstitutional; (3) the statute resulted in the arbitrary and capricious imposition of the death penalty; (4) the Utah Supreme Court unconstitutionally failed to apply the Wood decision retroactively; (5) his death sentence is improper under Enmund v. Florida, 458 U.S. 782, 102 S.Ct. 3368, 73 L.Ed.2d 1140 (1982), because there was no finding that he intended to kill; (6) Utah’s provision for execution before a firing squad violates the Establishment Clause; and (7) this method of execution constitutes cruel and unusual punishment.
The district court concluded that no evidentiary hearing was required to reach a decision, see Andrews IV, 600 F.Supp. at 415-16, declined to resolve the issue of procedural default, see id. n. 4, and ruled against Andrews on the merits of his claims, see id. at 415-32. Accordingly, the court denied Andrews’ petition for a writ of habeas corpus and dismissed the action. See id. at 432. This appeal followed. With the State’s consent, see Transcript of Oral Argument at 31-33, we withheld our resolution of the case pending the Supreme Court’s decision in Cabana v. Bullock, — U.S. -, 106 S.Ct. 689, 88 L.Ed.2d 704 (1986).
II.
FAIRNESS OF ANDREWS’ TRIAL
Andrews asserts that adverse publicity and hostile community sentiment undermined his right to a fair trial, and that he is entitled to a federal evidentiary hearing on this claim. Having reviewed the briefs and the appellate record, we conclude that no hearing is required under the principles of Townsend v. Sain, 372 U.S. 293, 83 S.Ct. 745, 9 L.Ed.2d 770 (1963), and that the constitutional standard for a fair trial has been met. We agree with the district court’s treatment of these two issues. Accordingly, we adopt the relevant portion of that court’s opinion as our own. See Andrews IV, 600 F.Supp. at 415-20.
III.
CONSTITUTIONALITY OF UTAH DEATH PENALTY STATUTE
We next address Andrews’ claim that the Utah death penalty statute is unconstitutional. The Supreme Court has mandated that the discretion inherent in capital sentencing decisions “must be suitably directed and limited so as to minimize the risk of wholly arbitrary and capricious action.” Gregg v. Georgia, 428 U.S. 153, 189, 96 S.Ct. 2909, 2932, 49 L.Ed.2d 859 (1976) (opinion of Stewart, Powell and Stevens, JJ.); accord Zant v. Stephens, 462 U.S. 862, 874, 103 S.Ct. 2733, 2741, 77 L.Ed.2d 235 (1983). Although the constitutionality of capital punishment laws ultimately turns on an examination of each distinct system, e.g., Pulley v. Harris, 465 U.S. 37, 45, 104 S.Ct. 871, 876, 79 L.Ed.2d 29 (1984); Zant, 462 U.S. at 874-75, 103 S.Ct. at 2741, the Supreme Court has emphasized several points which guide our consideration of this case.
A valid capital punishment statute must prescribe aggravating circumstances or their equivalent which genuinely narrow the class of persons who are subject to execution. Zant, 462 U.S. at 876-78, 103 S.Ct. at 2742-43; Godfrey v. Georgia, 446 U.S. 420, 428-29, 100 S.Ct. 1759, 1764-65, 64 L.Ed.2d 398 (1980) (plurality opinion); accord Pulley, 465 U.S. at 53,104 S.Ct. at 881; Jurek v. Texas, 428 U.S. 262, 270-71, 96 S.Ct. 2950, 2955-56, 49 L.Ed.2d 929 (1976) (opinion of Stewart, Powell, and Stevens, JJ.); Proffitt v. Florida, 428 U.S. 242, 250 & n. 8, 256 n. 14, 96 S.Ct. 2960, 2965 & n. 8, 2968 n. 14, 49 L.Ed.2d 913 *1261(1976) (opinion of Stewart, Powell, and Stevens, JJ.). If the prosecution establishes that a defendant’s crime fits at least one of these legislatively defined categories, the sentencing body may consider relevant non-statutory aggravating factors, see California v. Ramos, 463 U.S. 992, 1008, 103 S.Ct. 3446, 3457, 77 L.Ed.2d 1171 (1983); Zant, 462 U.S. at 878, 103 S.Ct. at 2743, and must be allowed to consider any mitigating evidence before deciding on a death sentence, see Lockett v. Ohio, 438 U.S. 586, 604, 98 S.Ct. 2954, 2964, 57 L.Ed.2d 973 (1978); accord Eddings v. Oklahoma, 455 U.S. 104, 110-12, 102 S.Ct. 869, 874-75, 71 L.Ed.2d 1 (1982). The sentencing phase of a capital case thus involves an individualized determination of the appropriate penalty based upon relevant characteristics of the defendant and the circumstances of his offense. Ramos, 463 U.S. at 1006, 103 S.Ct. at 3456; Zant, 462 U.S. at 879, 103 S.Ct. at 2743. Notwithstanding the wide range of information the jury may consider, its ultimate exercise of discretion is invariably focused through instruction on the various factors. See, e.g., Pulley, 465 U.S. at 53, 104 S.Ct. at 881; Proffitt, 428 U.S. at 258, 96 S.Ct. at 2969; Gregg, 428 U.S. at 197-98, 96 S.Ct. at 2936.
The Court has upheld only sentencing schemes that provide for some form of meaningful appellate review. See Pulley, 465 U.S. at 54-59, 104 S.Ct. at 881-884 (Stevens, J., concurring in part and in the judgment) (reviewing cases). A jury need not make specific written findings of aggravating and mitigating circumstances for purposes of review if the sentencing mechanism is otherwise valid. See Jurek, 428 U.S. 262, 96 S.Ct. at 2952 (juries required only to answer three general questions in order to impose death penalty).
A. The Utah Statute
We hold that Utah’s statutory sentencing scheme is constitutional. The State has restricted capital homicides to intentional or knowing murders committed under eight aggravating circumstances.1 See Utah Code Ann. § 76-5-202 (1973) (current version at § 76-5-202 (1986 Supp.)). These circumstances are elements of the crime of first degree murder. One or more must therefore be proved beyond a reasonable doubt in the guilt phase of a capital case.
First degree murder is punishable by death or life imprisonment, see id. § 76-3-206 (1973), and a separate hearing takes place upon conviction to determine a defendant’s sentence, see id. § 76-3-207(1) (1973) (current version at § 76-3-207 (1986 Supp.)). The parties may present evidence on any matter the court deems relevant to sentencing, “including but not limited to the nature and circumstances of the crime, the defendant’s character, background, history, mental and physical condition, and any other facts in aggravation or mitigation of the penalty.” Id. § 76-3-207(1) (1973). Aggravating circumstances include, but are not limited to, those listed as *1262elements of first degree murder. See id. Section 76-3-207(1) specifies six mitigating circumstances and authorizes the consideration of any other mitigating factors.2 See id. Although the statute mandates no particular burden of proof, the Utah Supreme Court held in connection with this case that the totality of evidence of aggravating circumstances must outweigh the totality of mitigating circumstances by a preponderance of the evidence in order to impose the death penalty.3 See Pierre, 572 P.2d at 1347-48. The court or jury which convicts a capital defendant determines his sentence, although the defendant may waive the jury at the penalty phase and be sentenced by the court. Utah Code Ann. § 76-3-207(1) (1973). A jury verdict imposing the death penalty must be unanimous. Id. § 76-3-207(2) (1973).
A capital defendant who has been sentenced to death may appeal to the Utah Supreme Court. Pierre, 572 P.2d at 1345; see also Utah Code Ann. § 76-3-207(3) (1973) (current version at § 76-3-207(4) (1986 Supp.)). That court conducts “a comprehensive review of the entire case, including a review of a sentence of death to determine if that sentence resulted from prejudice or arbitrary action or was disproportionate to the [crime].” Pierre, 572 P.2d at 1345. Furthermore, the court considers prejudicial errors which are neither assigned nor argued. See id. n. 9 (citing State v. Stenback, 78 Utah 350, 2 P.2d 1050 (1931)); State v. St. Clair, 3 Utah 2d 230, 282 P.2d 323, 327 (1955).
Utah has limited the class of defendants subject to execution by requiring that a jury find at least one statutory aggravating circumstance beyond a reasonable doubt in the guilt phase of a first degree murder trial. See Pierre, 572 P.2d at 1348. A prescribed list of relevant factors guides the jury's ultimate sentencing decision, and the requirement that aggravating outweigh mitigating circumstances directs the jury to focus upon factors favoring leniency versus death. The jury’s discretion is “suitably directed and limited so as to minimize the risk of wholly arbitrary and capricious action.” Gregg, 428 U.S. at 189, 96 S.Ct. at 2932 (opinion of Stewart, Powell, and Stevens, JJ.). Appellate review of the entire case ensures that discretion has not been exercised arbitrarily. This form of capital punishment law is constitutionally permissible under prevailing Supreme Court decisions. See, e.g., Pulley, 465 U.S. at 53, 104 S.Ct. at 881; Jurek, 428 U.S. at 276, 96 S.Ct. at 2958.
B. Additional Issues
Andrews raises numerous objections to the Utah statutory scheme, most of which we have considered and implicitly rejected in discussing the statute as a whole. Two remaining issues warrant further discussion. Andrews argues that the jury may have convicted him on the basis of an invalid statutory aggravating circumstance, and that the instructions given in the sentenc*1263ing phase did not provide the jury with adequate guidance.4
1. Killing for Personal Gain
Andrews argues that one of the aggravating circumstances submitted to the jury in this case, killing for personal gain, cannot withstand scrutiny.5 He contends that this aggravating circumstance is constitutionally overbroad because practically every deliberate homicide could be viewed as committed for the benefit of the perpetrator. The State responds that even if “killing for personal gain” is overbroad, the trial judge cured the problem by narrowly defining the term when he instructed the jury. His instruction stated:
“A killing for personal gain is defined in law as a killing so as to gain a substantial advantage or to rid oneself of substantial difficulty. It would be killing for personal gain if the motive for the killing was to silence a witness, prevent the discovery and prosecution of a crime, or to hide the identity of a perpetrator of crime because the escaping of such prosecution would be considered in law as personal gain.”
Rec., vol. XVI, state trial rec., vol. R-3, at 352. The district court held that this instruction satisfied constitutional concerns. See Andrews IV, 600 F.Supp. at 424.
We do not reach the merits of this contention because Andrews failed to preserve this claim in state court. When “a defendant has failed to abide by a State’s procedural rule requiring the exercise of legal expertise and judgment, ... [he] may not obtain federal habeas corpus relief absent a showing of ‘cause and actual prejudice.’ ” Reed v. Ross, 468 U.S. 1, 11, 104 S.Ct. 2901, 2908, 82 L.Ed.2d 1 (1984) (quoting Engle v. Isaac, 456 U.S. 107, 129, 102 S.Ct. 1558, 1572, 71 L.Ed.2d 783 (1982)). Andrews argues that he is entitled to an evidentiary hearing on the question of cause. However, we need not decide whether Andrews could satisfy the cause requirement because we conclude for the following reasons that he was not prejudiced.
Even if the “personal gain” aggravating circumstance is constitutionally overbroad, we are required to sustain Andrews’ death sentences because of the unimpeachable presence of two other statutory grounds. The case was submitted to the jury on six theories of aggravation. See supra note 5. Although the jury did not specify which of these aggravating circumstances it had found, the Eighth Amendment does not require a jury to identify the aggravating circumstances it has relied upon to convict a capital defendant under a statute such as Utah’s. See Jurek, 428 U.S. at 265 n. 1, 267-68, 96 S.Ct. at 2953 n. 1, 2954.
When one of the charged circumstances later proves invalid or unsupported by the record, however, the validity of the death sentence “depends on the function of the jury’s finding of an aggravating circumstance under [the State’s] capital sentencing statute, and on the reasons that the aggravating circumstance at issue in [the] particular case was found to be invalid.” Zant, 462 U.S. at 864, 103 S.Ct. at 2736. Here, like the Georgia statute in Zant, aggravating circumstances function in the guilt phase to narrow the class of persons who may be sentenced to death. See id. at 874, 879, 103 S.Ct. at 2741, 2743.
In Zant, the Court was clearly concerned with the reliability of the jury’s determination that the death penalty was appropri*1264ate. “[B]ecause there is a qualitative difference between death and any other permissible form of punishment, ‘there is a corresponding difference in the need for reliability in the determination that death is the appropriate punishment in a specific case.’ ” Id. at 884-85, 103 S.Ct. at 2746-47 (quoting Woodson v. North Carolina, 428 U.S. 280, 305, 96 S.Ct. 2978, 2991, 49 L.Ed.2d 944 (1976) (opinion of Stewart, Powell, and Stevens, JJ.)). The Georgia statute at issue in Zant required juries to specify in writing the statutory aggravating circumstances upon which they had relied. The Court could thus be certain that the challenged death sentence rested upon valid circumstances which had been found by the jury in addition to the one later held invalid.
The jury’s determination in this case is reliable notwithstanding the general verdict of guilt. Because Andrews and Pierre were each convicted of three murders, the jury could not have failed to find the aggravating circumstance of multiple killings. See supra note 5. Similarly, because they were convicted of aggravated robbery, the jury was compelled to find the circumstance of killing in perpetration of robbery. See id. Andrews’ convictions therefore rest upon at least two well-founded statutory aggravating circumstances which, under the Utah statute, place him in the restricted class of defendants who may be sentenced to death.
The Court in Zant also satisfied itself that all evidence relating to the invalid circumstance was otherwise fully admissible at the sentencing phase. See Zant, 462 U.S. at 886-87, 890, 103 S.Ct. at 2747-48, 2749. Similarly, the instant case is not one where inadmissible or prejudicial evidence was improperly admitted in connection with the statutory aggravating circumstance of killing for personal gain. Any evidence of killing for personal gain was admissible as evidence of the crime and also admissible as evidence of non-statutory aggravating circumstances under Utah Stat. Ann. § 76— 3-207(1) (1973). See Zant, 462 U.S. at 885-91, 103 S.Ct. at 2747-50; cf. Smith v. Murray, — U.S.-, 106 S.Ct. 2661, 2676-77 & n. 24, 91 L.Ed.2d 434 (1986) (Stevens, J., dissenting) (introduction of highly prejudicial, inadmissible evidence represents independent constitutional violation); Barclay v. Florida, 463 U.S. 3418, 103 S.Ct. 3418, 77 L.Ed.2d 1134 (1983).
In sum, Andrews can not establish the prejudice necessary to overcome his procedural default.
2. Sufficiency of sentencing instructions
Andrews also argues that the instructions in the sentencing phase were insufficient with regard to the proper weight to be accorded aggravating and mitigating circumstances. Appropriate sentencing instructions in a capital case guide the jury in its deliberations and focus attention upon the relevant factors to be considered. When at least one statutory aggravating circumstance has been established, “specific standards for balancing aggravating against mitigating circumstances are not constitutionally required.” Zant, 462 U.S. at 876 n. 13, 103 S.Ct. at 2742 n. 13 (emphasis added); see also Ford v. Strickland, 696 F.2d 804, 817-19 (11th Cir.) (en banc), cert. denied, 464 U.S. 865, 104 S.Ct. 201, 78 L.Ed.2d 176 (1983). Thus, sentencing authorities may determine a defendant’s fate without regard for burdens of proof or other measures of certainty.
At the same time, a jury should be instructed that the law recognizes circumstances which may be considered as extenuating or otherwise reducing a defendant’s culpability and hence his punishment. See Spivey v. Zant, 661 F.2d 464, 471 & n. 8 (5th Cir.1981), cert. denied, 458 U.S. 1111, 102 S.Ct. 3495, 73 L.Ed.2d 1374 (1982); accord Goodwin v. Balkcom, 684 F.2d 794, 800-03 (11th Cir.1982), cert. denied, 460 U.S. 1098, 103 S.Ct. 1798, 76 L.Ed.2d 364 (1983). In Spivey, the court overturned a death sentence where the state trial judge had instructed on the existence of aggravating circumstances while failing to mention that countervailing considerations might counsel in favor of leniency. See Spivey, 661 F.2d at 472. The Eleventh *1265Circuit recently reaffirmed its holding in Spivey and further held:
“[T]he Constitution requires that there be no reasonable possibility that a juror will misunderstand the meaning and function of mitigating circumstances, i.e., that the law recognizes the existence of circumstances which in fairness or mercy may be considered as extenuating or reducing the punishment.”
Peek v. Kemp, 784 F.2d 1479, 1494 (11th Cir.1986) (en banc); see also id. n. 16; People v. Brown, 40 Cal.3d 512, 220 Cal.Rptr. 637, 709 P.2d 440, 452-53 (1985) (en banc) (jury instructed not to consider sympathy for defendant), cert. granted sub nom. California v. Brown, — U.S. -, 106 S.Ct. 2274, 90 L.Ed.2d 717 (1986).
The sentencing instructions in this ease provided sufficient guidance. The Utah statute identifies and lists both aggravating and mitigating circumstances. See supra pp. 1261-62 & notes 2, 3. The trial judge recited the statutory mitigating circumstances, although he did not label them as such or explain their meaning and function.6 Three aspects of his charge distinguish this case from Spivey. First, the judge did not stress the significance of aggravating circumstances but simply listed the relevant factors. Second, at the close of this list, he directed the jury to consider “[a]ny other factor in mitigation or aggravation that would be considered by a responsible person____” See supra note 6. Finally, and most importantly, he instructed the jury to weigh these various factors and required the State to bear the burden of demonstrating that death was the appropriate penalty.7 These instructions emphasized that mitigating factors should be considered and that they could prove decisive in the balancing process. The jury was thus informed of its duty to decide between leniency and death on the basis of mitigating as well as aggravating evidence. Accordingly, we reject Andrews’ challenge to the sentencing instructions.
IV.
ALLEGED RACIAL DISCRIMINATION
Andrews contends that the Utah death penalty statute has failed in practice to alleviate the arbitrariness that marked the administration of capital punishment prior *1266to Furman v. Georgia, 408 U.S. 238, 92 S.Ct. 2726, 33 L.Ed.2d 346.8 In this context, arbitrariness can mean either purely random application of the death penalty, or its imposition on the basis of a legally irrelevant factor such as race. Compare id. at 309-10, 92 S.Ct. at 2762 (Stewart, J., concurring), and id. at 312-13, 92 S.Ct. at 2763-64 (White, J., concurring), with id. at 249-57, 92 S.Ct. at 2731-35 (Douglas, J., concurring), and id. at 364-66, 92 S.Ct. at 2790-91 (Marshall, J., concurring). Andrews, a black, claims that racial discrimination impermissibly taints capital punishment in Utah. On appeal, he argues that the district court erred in denying him an evidentiary hearing on this issue.
A hearing would be necessary to receive “any evidence that a particular defendant was discriminated against because of his race.” McCleskey v. Kemp, 753 F.2d 877, 894 (11th Cir.1985) (en banc) (emphasis added), cert. granted, — U.S.-, 106 S.Ct. 3331, 92 L.Ed.2d 737 (1986). Conclusory allegations will not suffice to warrant a hearing. See, e.g., Bashor v. Risley, 730 F.2d 1228, 1233-34 (9th Cir.), cert. denied, 469 U.S. 838, 105 S.Ct. 137, 83 L.Ed.2d 77 (1984). A habeas petitioner must provide supporting factual allegations. See Townsend v. Sain, 372 U.S. at 312, 83 S.Ct. at 756.
Andrews’ submissions are inadequate to indicate that evidence of discrimination at his trial would be forthcoming if a hearing were held. He alleges adverse treatment by the prosecution, a racially hostile atmosphere at trial, and bias stemming from improper contact with the jury. We have considered and rejected several of Andrews’ claims in deciding that he received a fair and impartial jury trial.9 We add only that the prosecution and defense received ample opportunity to question prospective jurors about racial prejudice, see Turner v. Murray, — U.S.-, 106 S.Ct. 1683, 90 L.Ed.2d 27 (1986), and that the jury did not convict Keith Roberts of murder even though he too is black and participated in the robbery which culminated in the murders. To the extent that Andrews presents other issues, his allegations are conclusory and therefore insufficient to warrant a hearing.
Andrews seeks to bolster his position by alleging that Utah’s sentencing scheme as a whole imposes the death penalty disproportionately on blacks. In McCleskey, the Eleventh Circuit sitting en banc considered the doctrinal basis of race discrimination claims in capital cases, the utility of statistical evidence in evaluating such claims, and the circumstances under which an evidentiary hearing must be granted. The majority observed that a claim of discriminatory sentencing could be framed alternatively as cruel and unusual punishment, as a denial of equal protection, and as a violation of due process. See 753 F.2d at 890-92. Whichever was chosen, the majority held that: *1267Id. at 892. The majority reasoned that because Furman invalidated only those capital sentencing schemes that operate in an arbitrary fashion, appropriate procedural safeguards will prevent such a result and allow only the possibility of intentional discrimination. See id. at 890-92. An evidentiary hearing need not be granted, the majority added, unless a valid statistical study purports to demonstrate a great enough disparity to indicate intentional discrimination. See id. at 892-93; accord Ross v. Kemp, 756 F.2d 1483, 1491 (11th Cir.1985) (en banc).
*1266“proof of a disparate impact alone is insufficient to invalidate a capital sentencing system, unless that disparate impact is so great that it compels a conclusion that the system is unprincipled, irrational, arbitrary and capricious such that purposeful discrimination — i.e., race is intentionally being used as a factor in sentencing — can be presumed to permeate the system.”
*1267The principal dissenting opinion took a different approach. The dissent interpreted the Supreme Court’s death penalty decisions as establishing that a statewide pattern of arbitrary sentencing, particularly one skewed on the basis of irrelevant factors such as race, would violate the Eighth Amendment. See McCleskey, 753 F.2d at 910 (Johnson, J., dissenting in part and concurring in part). The dissent further emphasized the importance of ensuring fairness when a defendant’s life is at stake. Discretionary sentencing, even under a system with procedural safeguards, permits arbitrariness to play a role yet makes it exceedingly difficult to detect. Statistically significant evidence of disparate impact must therefore be relied upon. Focusing upon intent and setting a correspondingly high standard of proof, the dissent implied, condones potentially serious unfairness.
In our view, a pattern of discriminatory or otherwise arbitrary sentencing decisions in capital cases can violate the Constitution regardless of intent.10 Unlike the Fourteenth Amendment’s guarantee of “equal laws, not equal results,” Personnel Administrator v. Feeney, 442 U.S. 256, 273, 99 S.Ct. 2282, 2293, 60 L.Ed.2d 870 (1979) (sex discrimination), the Eighth Amendment protects against unacceptably inconsistent outcomes. The Furman Court invalidated existing death penalty laws not because of the mental state of government officials or jurors but because, as the laws were structured and administered at the time, they failed in practice to distinguish fairly between those who received death sentences and those who did not. See Gregg, 428 U.S. at 222-23, 96 S.Ct. at 2947-48 (White, J., concurring in judgment). Each of the concurring opinions in Furman relied upon various forms of statistical evidence that purported to demonstrate patterns of random or discriminatory sentencing without regard for an actor’s purpose or motive. See Furman, 408 U.S. at 249-52, 92 S.Ct. at 2731-33 (Douglas, J., concurring); id. at 291-95, 92 S.Ct. at 2753-55 (Brennan, J., concurring); id. at 309-10, 92 S.Ct. at 2762 (Stewart, J., concurring); id. at 313, 92 S.Ct. at 2764 (White, J., concurring); id. at 364-66, 92 S.Ct. at 2790-91 (Marshall, J., concurring).
These invalidated statutes contained none of the procedural safeguards which have since been adopted. The decisive question, however, is not whether constitutionally mandated safeguards exist, but whether they work. We do not believe that Furman would have been decided differently had the challenged statutes embodied substantial safeguards but yielded no less random or discriminatory results. *1268Pre-Furman statutes were struck down because they failed to generate acceptably consistent outcomes. The intent of actors within the system is not necessarily relevant to the fulfillment of this paramount objective.
The Court has expressly affirmed this conception of the Eighth Amendment in its decisions following Furman. Thus “if a State wishes to authorize capital punishment it has a constitutional responsibility to tailor and apply its law in a manner that avoids the arbitrary and capricious infliction of the death penalty.” Godfrey, 446 U.S. at 428, 100 S.Ct. at 1764; see also Gregg, 428 U.S. at 195 n. 46, 96 S.Ct. at 2935 (opinion of Stewart, Powell, and Stevens, JJ.). Statutory sentencing schemes that provide for appropriate procedural safeguards have been upheld because they “promised to alleviate” arbitrariness. See Zant v. Stephens, 456 U.S. 410, 413, 102 S.Ct. 1856, 1857, 72 L.Ed.2d 222 (1982) (per curiam); see also Barclay v. Florida, 463 U.S. 939, 960, 103 S.Ct. 3418, 3430, 77 L.Ed.2d 1134 (1983) (Stevens, J., concurring in the judgment). The constitutionality of such laws therefore depends upon their success in fulfilling this promise. The Court’s decisions mandate that “capital punishment be imposed fairly, and with reasonable consistency, or not at all.” Ed-dings, 455 U.S. at 112, 102 S.Ct. at 875. Moreover, “[i]t is of vital importance ... that any decision to impose the death sentence be, and appear to be, based on reason rather than caprice or emotion.” Gardner v. Florida, 430 U.S. 349, 358, 97 S.Ct. 1197, 1204, 51 L.Ed.2d 393 (1977) (opinion of Stevens, J.). Death is unique among criminal sanctions, and we therefore insist upon a correspondingly higher degree of reliability, consistency, and fairness in capital sentencing decisions. See, e.g., Zant, 462 U.S. at 884-85, 103 S.Ct. at 2746-47.
This objective is best accomplished by holding that a pattern of inconsistent sentencing decisions can violate the Eighth Amendment. Juries retain considerable discretion in capital cases. Although the narrowing function served by statutory aggravating circumstances and the availability of appellate review help to ensure that the death penalty will be warranted whenever it is imposed, the additional risk remains that juries will sentence some defendants to death while sparing others who are no less culpable. The pivotal opinions in Furman rested upon a perception of just such systemic unfairness, see Fur-man, 408 U.S. at 309-10, 92 S.Ct. at 2762 (Stewart, J., concurring); id. at 313, 92 S.Ct. at 2764 (White, J., concurring), and it is exceedingly difficult to assess whether this risk has been adequately guarded against. An inquiry into the intent of juries appears all but impossible. On the other hand, properly designed statistical analyses would facilitate such assessments by accounting for all capital cases and determining to what extent the death penalty is imposed, or not imposed, on the basis of relevant characteristics of the defendant and the circumstances of his offense. Evidence of inconsistent results, of sentencing decisions that cannot be explained on the basis of individual culpability, would indicate that the system is not operating fairly and therefore may violate the Eighth Amendment.
Reading Furman narrowly, the McCleskey majority insists that only an extreme fact pattern like that presented in Furman can violate the Eighth Amendment. Reading Furman broadly, the dissent would arguably prohibit any statistically significant pattern of random or discriminatory sentencing decisions. See McCleskey, 753 F.2d at 911 & n. 8 (opinion of Johnson, J.). We believe there is an appropriate middle ground. Determining the degree of racially disparate impact that violates the Constitution calls for a court’s judgment as well as a statistician’s findings. Statistically significant results may not always compel the legal conclusion that a statutory sentencing scheme is unconstitutional. In our view, however, statistical findings of the kind proffered in McCleskey would warrant such a conclusion. When a defendant is twenty percent more likely to receive the death penalty for committing a moderately aggravated homicide, for the sole reason *1269that his victim was white rather than black, see id. at 913-14, the system under which he is sentenced produces unreasonably inconsistent outcomes.
We need not decide precisely what degree of disparate impact would warrant condemning a capital punishment system because Andrews has not made a sufficient showing to call into question the overall fairness of the statutory scheme under which he received the death penalty. Constitutionally adequate procedures to direct and limit discretion in imposing the death penalty raise a presumption that a capital punishment law operates evenhandedly. See McCleskey, 753 F.2d at 897 (presumed that statute operates in constitutional manner). This presumption must be rebutted by proof of either random or systematically disparate sentencing patterns. Such proof should generally consist of an appropriately formal study that generates statistically significant results while accounting for the effect of other causal variables. See, e.g., Gross & Mauro, Patterns of Death: An Analysis of Racial Disparities in Capital Sentencing and Homicide Victimization, 37 Stan.L.Rev. 27 (1984). Proffering such a study would create a “reasonable possibility” of establishing a basis for relief and therefore would entitle a federal habeas corpus petitioner to an evidentiary hearing under the principles of Townsend v. Sain. See Ross, 756 F.2d at 1495 n. 1 (Johnson, J., dissenting in part and concurring in part).
In this case, Andrews alleged the following in his habeas petition:
“Three of the four persons presently under death sentence in Utah are black, although black people make up less than one percent (1%) of the population of Utah, and a small fraction of Utah murder defendants. Every person sentenced to death under the present Utah law has been an impoverished male whose alleged victim was Caucasian. In every case tried under the present Utah statute in which a black person has been charged with murdering a white victim, the case has proceeded to a death sentencing phase; in all but one of those cases, a death sentence has been imposed. In no case in which a non-white person has been a victim of a capital homicide, has a death sentence been imposed, although numerous such cases have been eligible for capital sentences.”
Rec., vol. VI, at 1112. The district court held that these small numbers preclude valid statistical analysis. On appeal, Andrews has submitted more current data showing that four of the seven individuals now on Utah’s death row are black, still a small population. Although it may be correct that small numbers make predictions difficult, see generally Gross & Mauro, 37 Stan.L.Rev. at 93, we are not inclined to condone existing discrimination until enough others have been sentenced and executed to produce a population large enough to analyze. The existence of a small sample should not result in the denial of constitutional rights simply because of the time and place of a defendant’s sentence.
However, a small population is not the only problem with Andrews’ proffer. He has not developed the evidence that is available so as to provide some factual basis for relief. More importantly, Andrews has failed to address whether other causal factors, such as the degree of aggravation involved in the murders, might account for the sentences of the seven individuals now on Utah’s death row. Having collected reports on cases in which the death penalty was withheld, Andrews has neither analyzed these data nor obtained less formal evidence of historical patterns of discriminatory sentencing in the twelve years since his original trial.
Absent careful analysis of sentencing patterns in Utah, we have no basis to conclude that anyone on death row is there because of systemic racial discrimination. In the Georgia study done in McClesky, no sentencing disparity was shown based on the race of the defendant. See McCleskey, 753 F.2d at 899. Instead, a statistically disproportionate number of defendants received the death penalty when their victims were white rather than black. Id. at 896. *1270Moreover, the study showed that the race-of-the-victim disparity in Georgia was acute only in those cases where the degree of aggravation involved was in the mid-range. Id. In highly aggravated circumstances, the killers of both white and black victims were likely to receive in the death penalty. Id. Andrews himself participated in a crime that involved multiple killings and torture of the victims. None of his proffered evidence even remotely suggests the presence of racial discrimination where such highly aggravated murders are concerned. And nothing has been offered to show that the seven individuals on Utah’s death row committed less aggravated murders.
In Andrews’ particular case, moreover, we find ample indication that the jury sentenced Andrews to death for reasons other than his race or the race of the victims. We have canvassed at length the procedural safeguards employed in this case. The court conducted extensive voir dire on the issue of race to ensure an unprejudiced jury. It gave proper instructions requiring the jury to focus on “the character of the individual and the circumstances of the crime.” See Zant, 462 U.S. at 879, 103 S.Ct. at 2744. Andrews was permitted to introduce any evidence he chose in mitigation. Most importantly, Andrews’ black co-defendant Roberts was not convicted of murder, which strongly indicates that the jury did not reach its verdict for reasons of race. Given these indicia of reliability in the jury’s decision to give Andrews the death sentence, together with the absence of evidence indicating a racially disparate impact within the class of highly aggravated murders, we conclude that Andrews is not entitled to an evidentiary hearing on his claim of racially discriminatory sentencing.
V.
RETROACTIVITY OP WOOD DECISION
Andrews argues that the Supreme Court of Utah violated his federal constitutional rights when it applied retroactively its decision in State v. Wood, 648 P.2d 71, to capital cases pending on direct appeal but not to cases like his that were already final. While no specific standard for balancing aggravating and mitigating circumstances is constitutionally required, Wood established as a matter of state law that aggravating circumstances must outweigh mitigating circumstances beyond a reasonable doubt before the death penalty may be imposed. Andrews sought and was denied retroactive relief under this decision. See Andrews III, 677 P.2d 81. Three years later, the court applied Wood retroactively to cases which, unlike those of Andrews and Pierre, were pending on direct appeal when Wood was decided. See State v. Norton, 675 P.2d 577, 583-84 (Utah 1983), cert. denied, 466 U.S. 942, 104 S.Ct. 1923, 80 L.Ed.2d 470 (1984). Andrews contends that the court denied him equal protection by arbitrarily treating him differently from others similarly situated and that its actions were not based on established principles of retroactivity. We disagree.
The Constitution “neither prohibits nor requires” the retroactivity of judicial decisions. Linkletter v. Walker, 381 U.S. 618, 629, 85 S.Ct. 1731, 1737, 14 L.Ed.2d 601 (1965); Great Northern Railway Co. v. Sunburst Oil & Refining Co., 287 U.S. 358, 364, 53 S.Ct. 145, 148, 77 L.Ed. 360 (1932). “A state in defining the limits of adherence to precedent may make a choice for itself between the principle of forward operation and that of relation backward.” Sunburst Oil, 287 U.S. at 364, 53 S.Ct. at 148. Either choice affords due process of law. Id. at 363-64, 53 S.Ct. at 148.
The Due Process and Equal Protection Clauses permitted the Utah court to distinguish between cases on direct appeal and those seeking collateral relief, and to apply Wood retroactively to one class but not the other.11 The court drew a rational *1271distinction in concluding that the State’s interest in the finality of criminal convictions warranted retroactive application only to direct appeals. See Norton,. 675 P.2d at 583-84; cf. Shea v. Louisiana, 470 U.S. 51, 105 S.Ct. 1065, 1070, 84 L.Ed.2d 38 (1985) (decision regarding illegal confessions applies retroactively to cases pending on direct appeal at time decision rendered). As a case of first impression, moreover, Andrews III conflicted with no Utah precedent concerning the retroactive application of judicial decisions to criminal cases that were already final. Andrews protests that he and Pierre alone did not receive the benefit of the standard announced in Wood. Although perhaps understandable, this argument is unpersuasive in light of the court’s rational basis for drawing a distinction.12
A direct challenge to the retroactivity analysis of Andrews III affords no additional basis for relief. Employing federal precedent for purposes of guidance, the Utah Supreme Court decided the issue of Wood’s retroactivity to Andrews’ case as a matter of Utah law. See Andrews III, 677 P.2d at 88. It is settled that federal courts may not issue a writ of habeas corpus based upon a perceived error in such a decision. Pulley, 465 U.S. at 41, 104 S.Ct. at 874-75. Even if an exceptionally egregious error of state law could result in a denial of due process or equal protection, see id., this is not such a case. The court confronted a question of first impression in Utah, exhaustively analyzed relevant federal cases, and reached a reasonable result. After examining the totality of the circumstances, we find nothing to suggest that the court’s conclusion was dictated by this case rather than general principles of retroactivity. The court’s conclusion therefore does not warrant federal judicial intervention.13
VI.
VALIDITY OF ANDREWS’ DEATH SENTENCE UNDER ENMUND V. FLORIDA
Andrews finally contends that his death sentences should be overturned because he *1272did not intend that life would be taken.14 As we previously mentioned, the State agreed that we should wait for the decision in Cabana v. Bullock, — U.S.-, 106 S.Ct. 689, 88 L.Ed.2d 704 (1986), before deciding this issue.
The Eighth Amendment prohibits imposition of the death penalty upon one “who does not himself kill, attempt to kill, or intend that a killing take place or that lethal force will be employed.” Enmund v. Florida, 458 U.S. 782, 797, 102 S.Ct. 3368, 3376, 73 L.Ed.2d 1140 see also Cabana, 106 S.Ct. at 693, 697. A death sentence may rest upon a guilty verdict which necessitates a finding of intent, see Cabana, 106 S.Ct. at 695-96, or upon appropriate factual findings made by a state trial judge or appellate court, see id. at 696-97. If such a finding has been made, it is presumed correct in subsequent federal habeas proceedings. Id. at 697-98. If not, a federal court must afford the state court an opportunity to make the requisite finding. Id. at 699-700.
This case was tried and presented to the jury on a theory of intentional or knowing murder rather than felony murder. Compare Enmund, 458 U.S. at 789-90 & n. 7, 102 S.Ct. at 3372-73 & n. 7 (noting requirement of culpable mental state to impose death penalty in Utah), with Cabana, 106 S.Ct at 696 (case tried on theory of felony murder). The trial judge told the jury in instruction 8 that the prosecution must prove four elements in order to convict Andrews of capital homicide: (1) that the victim was killed intentionally or knowingly, (2) that an aggravating circumstance was present, (3) that the killing occurred at a certain time and place, and (4) that the defendant either killed or was responsible as a “party” to the crime. See rec., vol. XVI, state trial rec., vol. R-3, at 351-53. Because Pierre shot and killed each of the victims, the extent of Andrews’ culpability depends upon the circumstances under which the jury could have found him to be a party. The trial judge listed four such circumstances at the close of instruction 8:
“[Andrews] would be a party to murder if:
A. He actually and intentionally perpetrated the murder himself, or
B. He intentionally helped plan or assisted in the advancement of the murder with intent that it would take place, and did not effectively withdraw before the killing.
C. He intentionally rendered active advice during the murder, or
D. He intentionally helped the murderer escape from the immediate scene of the crime.
(The subject of ‘party’ is described in more detail in a later instruction)” Id. at 352-53.
In instruction 12, the trial judge defined “party” in greater detail:
“The statutes of Utah provide that: ‘Every person, acting with the mental state required for the commission of an offense, who directly commits the offense, who solicits, requests, commands, encourages, or intentionally aids another person to engage in conduct which constitutes an offense shall be criminally liable as a party for such conduct.’ “To be a principal in the accomplishment of a crime where the person under consideration is not the actual doer of the crime, such person’s participation must be intentional and with an intent that his act will further, or came the crime to come about, or make easier its completion. A person is not a principal in the crime if he supplies automobiles or weapons to a criminal not knowing that a *1273crime is going to be accomplished, or not knowing the general criminal conduct planned by the person who has receive'd the assistance. A person is a principal in a crime only if he intentionally has aided, encouraged, or assisted in its accomplishment. Assistance rendered after the crime is complete and escape from the immediate crime has been completed, does not make a person a principal of the crime even though he may be guilty of tampering with evidence or some other charge not here brought. In other words, if A commits a crime and B discovers that the crime has been committed and assists A in covering up the crime, B is not guilty as a principal because he is merely involved after the fact.
“A person is a party to a robbery, or rape, or theft, etc., and he is also a party to the killing that may occur therein, only if he knew the killing was planned, or knew it was planned if certain events occur during the crime which does in fact occur, because he has approved conduct containing a contingent plan to kill, or if he knows certain co-parties plan to kill if certain contingencies occur. He would not be a party to such a killing if he does not know of a plan to kill and only suspects such an event may possibly occur, but does not seriously expect it.”
Id. at 357 (emphasis added). The trial judge thus instructed that a party must act with the same mental state as that required for commission of the murder, including intent, and the judge otherwise made clear that Andrews must have acted with knowledge that his acts were furthering a deliberate homicide. We note in addition that the judge’s initial instruction on the elements of first degree murder, instruction 8, specifically referred to this supplementary instruction defining “parties”; that the judge further charged that his instructions should be considered as a whole and of equal importance regardless of their order, see id. at 370; and that the jurors had all of the instructions with them during their deliberations.
In this context, we reject Andrews’ arguments that the instructions permitted his conviction for first degree murder without a sufficient finding that he personally intended to kill or intended that life would be taken. He contends there are several alternative scenarios under which the jury could have convicted him without the requisite finding of intent. One alternative focuses upon instruction 13, in which the court instructed the jury that if one plans or assists in the planning of a murder, he has the affirmative duty of either informing the police or destroying his contribution to the crime in order to withdraw effectively and thereby avoid responsibility for capital homicide. See infra n. 15. Andrews argues that the jury could have impermissibly found him guilty of capital homicide even if he only assisted early in the crime and had a change of heart, but did not effectively withdraw within the meaning of instruction 13.15 For the following reasons, we disagree.
Andrews’ trial counsel argued in his closing remarks to the jury that while there may have been a plan to commit robbery, there was no premeditated plan to kill. He maintained that Pierre decided to kill only after the parents of two of the young shop *1274workers unexpectedly arrived on the scene, and that Andrews left the premises without ever knowing Pierre’s intention to dispose of the witnesses. As one alternative possibility, however, Andrews’ counsel contended that if the jury believed Andrews became aware of Pierre’s intention to kill, Andrews nonetheless immediately disassociated himself from that intention by leaving. In other words, Andrews’ theory was that he never participated or assisted in a plan to kill and that he withdrew his physical presence as soon as he learned of Pierre’s intentions, thus never forming the requisite intention. Thus, Andrews did not make a general objection to instruction 13, on withdrawal; he only objected specially that the example of supplying wares such as tools was too narrow. See supra note 15. In his objection, Andrews maintained that the example should be deleted, or broadened to include adding and then taking away one’s physical presence as the assistance to the crime. The court further alluded to withdrawal in instruction 14 and instructed that “[a]ny verbal or physical acts of withdrawal may be considered by the jury in determining whether taken in total, the verbal and physical acts of an accused demonstrates a withdrawal by him from the criminal act.” Rec., vol. XVI, state trial rec., vol. R-3, at 359. The state objected to this instruction on the ground that it overemphasized withdrawal, leaving us to conclude that Andrews sponsored the instruction.
No argument was made at trial or on appeal that even if Andrews formed an intent to kill, he changed his mind at the last minute. No instruction was requested by Andrews to permit the jury to reach such a conclusion. The argument throughout has instead been that the instructions permitted the jury to convict Andrews without finding he formed an intent to kill, and it is this conclusion with which we disagree. As we have previously concluded, Instruction 12 clearly required the jury to find that Andrews knew of the impending murders and that he had the same intention to kill as Pierre. Thus, Andrews’ physical withdrawal from the basement was done with the understanding that Pierre fully intended to kill the victims that he, Andrews, had just helped to capture, bind, poison, and rob. Under these circumstances, the trial judge’s instructions required a finding of culpability that comports fully with Enmund.
We also reject Andrews’ contention that the jury could have convicted him under instruction 8 by finding that he intentionally rendered advice during the murder or intentionally helped the murderer escape, without also finding that he intended the murders to occur. Both of these alternatives do mention intent only with respect to acts which may have had the effect of assisting Pierre; neither necessarily implies any particular mental state with respect to the murders themselves. See generally W. LaFave & A. Scott, Criminal Law § 64, at 504-05 (1972). Yet the clear requirement of instruction 12 that a party must act “with the mental state required for the commission of an offense” and “with an intent that his act will further, or cause the crime to come about” negates the possibility that the jury could have convicted Andrews without also making the requisite finding that he intended the murders. The jury’s failure to convict Roberts, who could readily be viewed as having intentionally assisted Pierre, confirms that the jury acted in accordance with the instructions as a whole and focused on Andrews’ intent that the murders take place.
The implicit finding of Andrews’ intent by a properly instructed jury, which must be presumed correct under Cabana, is supported by the record. Before the Hi-Fi robbery, Andrews said to an acquaintance that “one of these days I would like to rob a Hi Fi Shop and if anybody gets in my way I will kill them.” Rec., vol. XVI, state trial rec., vol. T-9, at 1549. Andrews assisted Pierre in capturing and binding the eventual victims. When they begged for mercy, Pierre considered in Andrews’ presence whether or not they should be killed. Andrews himself helped to administer what he either knew in advance to be Drano or discerned from the first victims’ reactions *1275to be a poison capable of inflicting grievous harm or death. Andrews did say, “I’m scared. I can’t do it.” Notwithstanding that such statements may suggest an unwillingness to kill, they also support a clear inference that Andrews knew of Pierre’s intention to do so. As Andrews was leaving the basement before the murders occurred, Pierre said to him “about thirty minutes,” which further suggests an awareness of what was about to happen. Although Andrews apparently left the shop, someone returned shortly thereafter to pick up Pierre. Andrews also participated in disposing of the stereo equipment and other property stolen from the store. The jury could thus have inferred that Andrews fully acquiesced in the murders even though he himself did not commit them. Under Enmund and Cabana, the death sentence is not disproportionate to Andrews’ knowledge of and participation in the offense.16
VIII.
CONCLUSION
We affirm the judgment of the district court denying Andrews’ petition for a writ of habeas corpus. Because this is a capital case, when the final order of this court is entered, following the consideration of any rehearing petition that may be filed, we will stay our mandate and the execution of Andrews’ death warrant for 30 days pending the filing of a petition for certiorari in the Supreme Court of the United States. If a petition for certiorari is filed within such time, then the stay of our mandate and of petitioner’s execution will continue until disposition by the Supreme Court of the petition for certiorari.
. The enumerated aggravating circumstances are:
"(a) The homicide was committed by a convict under sentence of imprisonment.
(b) At the time the homicide was committed the actor also committed another homicide.
(c) The actor knowingly created a great risk of death to a person other than the victim and the actor.
(d) The homicide was committed while the actor was engaged in the commission of, or an attempt to commit, or flight after committing or attempting to commit, robbery, rape, forcible sodomy, or aggravated sexual assault or arson, burglary or kidnapping.
(e) The homicide was committed for the purpose of avoiding or preventing an arrest by a peace officer acting under color of legal authority or for the purpose of effecting an escape from lawful custody.
(f) The homicide was committed for pecuniary or other personal gain.
(g) After having previously been convicted of first or second degree murder.
(h) The homicide was committed upon a child under the age of twelve years as the result of physical abuse or neglect.”
Utah Code Ann. § 76-5-202(1) (1973). The current statute lists seventeen aggravating circumstances. See id. § 76-5-202(1) (1986 Supp.). We express no opinion on its constitutionality but confine our attention to the 1973 statutes under which Andrews was sentenced.
. The enumerated mitigating circumstances are: "(a) The defendant has no significant history of prior criminal activity;
“(b) The murder was committed while the defendant was under the influence of extreme mental or emotional disturbance;
"(c) The defendant acted under extreme duress or under the substantial domination of another person;
"(d) At the time of the murder, the capacity of the defendant to appreciate the criminality (wrongfulness) of his conduct or to conform his conduct to the requirement of law was substantially impaired as a result of mental disease, intoxication, or influence of drugs;
"(e) The youth of the defendant at the time of the crime;
"(f) The defendant was an accomplice in the murder committed by another person and his participation was relatively minor;
“(g) And any other fact in mitigation of the penalty."
Utah Code Ann. § 76-3-207(1) (1973).
. Andrews and Pierre were sentenced according to jury instructions embodying this standard. See Pierre, 572 P.2d 1338. The Utah court has since decided that the sentencer must find beyond a reasonable doubt both that the aggravating circumstances outweigh those in mitigation, and that the death penalty is appropriate. See Wood, 648 P.2d 71.
. Andrews also claims that specific aggravating circumstances should have been alleged in the state’s charging documents. We disagree. Andrews could have requested a bill of particulars but failed to do so. In any event, statutory notice of aggravating circumstances satisfies constitutional requirements under the Due Process Clause. See Spinkellink v. Wainwright, 578 F.2d 582, 609-10 (5th Cir.1978), cert. denied, 440 U.S. 976, 99 S.Ct. 1548, 59 L.Ed.2d 796 (1979).
. The case was submitted under a total of six theories of aggravation: (1) multiple killings, (2) creating a great risk of death to persons other than the victim and defendant, (3) killing in perpetration of robbery, (4) killing in perpetration of rape, (5) killing for pecuniary gain, and (6) killing for personal gain. See rec., vol. XVI, state trial rec., vol. R-3, at 351-52.
. Instruction No. 4 reads in pertinent part as follows:
“You may consider the nature and circumstances of the crime, the character of the defendant, his background, his general personal history, his mental and physical condition, and other factors.
“You may consider
(a) Whether or not the defendant has any significant history of prior criminal activity;
(b) Whether or not murder was committed while the defendant was under the influence of any mental or emotional disturbance or duress;
(c) Whether or not the defendant acted under duress or substantial domination of another person;
(d) The general capacity of the defendant to appreciate the wrongfulness of his conduct, or the ability to conform his conduct to the standards required by law and whether or not such capacity was substantially impaired as a result of any mental disease, or intoxication;
(e) The youth of the defendant at the time of the crime;
(f) Whether or not the defendant was a party to the murder committed by another person and whether his participation was relatively minor or major;
(g) Any other factor in mitigation or aggravation that would be considered by a responsible person making such a decision in an appropriate manner.
Rec., vol. XVI, state trial rec., vol. R-3, at 414-15.
. Instructions No. 1 and No. 2 read in pertinent part:
"It is the duty of the court to instruct you in the law that applies to the sentence procedure____ On the other hand, it is your exclu-
sive province to determine the sentence in this case, and you should consider and weigh the factors mentioned in this instruction for that purpose. You may use the instructions given you in the case as they apply.
"You are instructed that it would be improper for you to again debate the question of guilt or innocence of any defendant already found guilty. There is no fixed standard as to the degree of persuasion needed for a particular sentence, as the law leaves that consideration to the jury but the burden of proof to satisfy the jury that a death sentence is appropriate is on the State.”
Rec., vol. XVI, state trial rec., vol. R-3, at 412 (emphasis added).
. The State contends that Andrews defaulted on this claim. However, the Utah Supreme Court considered the merits of the argument in the first state habeas case, notwithstanding the pri- or procedural default. See Andrews II, 607 P.2d at 822, 825. If a state court has reached the merits of a claim, a federal habeas court may do the same despite the existence of a state procedural bar. See, e.g., Morishita v. Morris, 702 F.2d 207, 209 (10th Cir.1983); see also County Court of Ulster County v. Allen, 442 U.S. 140, 147-54, 99 S.Ct. 2213, 2219-23, 60 L.Ed.2d 777 (1979).
. One incident involved a stick figure at the gallows that was labeled “Hang the Niggers.” Sketched on a napkin, this message was discovered by one or more jurors while on their lunch break at a local restaurant. The district court addressed the legal implications of this incident, see Andrews IV, 600 F.Supp. at 419-20, and we have adopted that court’s views in Part II of this opinion.
. Even if intent must be proved, we believe that the standard adopted by the majority in McCleskey is too stringent. While intent is difficult enough to prove, intent that permeates an entire sentencing system is practically beyond proof. Cf. Batson v. Kentucky, — U.S. -, 106 S.Ct. 1712, 1720-21 & n. 17, 90 L.Ed.2d 69 (1986) (overruling Swain v. Alabama, 380 U.S. 202, 85 S.Ct. 824, 13 L.Ed.2d 759 (1965), to extent it imposed "crippling burden of proof’ on defendants challenging discriminatory exercise of peremptory challenges). Capital defendants are often prepared to demonstrate not only that a disproportionate number of those sentenced to die are black themselves or are the killers of white victims but also that the disparity is statistically significant after accounting for the effect of other explanatory variables. A proffer of this kind meets or exceeds the threshold burden of proof in other contexts where intent must be proved. See, e.g., Castaneda v. Partida, 430 U.S. 482, 97 S.Ct. 1272, 51 L.Ed.2d 498 (1977) (selection of grand jury venires); Furnco Construction Corp. v. Waters, 438 U.S. 567, 98 S.Ct. 2943, 57 L.Ed.2d 957 (1978) (employment discrimination). To impose a higher burden, as McCleskey does, is anomalous even without invoking the need for added fairness in capital cases.
. Andrews also urges that racial bias accounts for the Utah Supreme Court’s decisions. We *1271reject this claim. Aside from the mistaken assertion that he and Pierre have been singled out for adverse treatment, see infra note 12, Andrews has proffered no evidence of the discriminatory intent presently required to prove a denial of equal protection, see, e.g., Washington v. Davis, 426 U.S. 229, 239-45, 96 S.Ct. 2040, 2047-50, 48 L.Ed.2d 597 (1976). Absent such evidence, we are confined to considering whether the court’s decisions were so inconsistent or unfounded that they violate the Constitution irrespective of intent.
. We note that, prior to Wood, death sentences apparently were imposed and affirmed on direct appeal in at least one other case involving the same standard under which Andrews and Pierre were sentenced. See State v. Codianna, 573 P.2d 343, 352 (Utah 1977) (consolidated appeals of three co-defendants), cert. denied, 439 U.S. 882, 99 S.Ct. 219, 58 L.Ed.2d 194 (1978); see also State v. Brown, 607 P.2d 261, 270 (Utah 1980) (adhering to same standard but reversing because no instruction given on burden of proof). Andrews makes the related point that, immediately after he and Pierre were sentenced, the state attorney general began to advise prosecutors to recommend a reasonable doubt standard. He appears to have taken this position, however, only after a later judicial opinion raised the subject and argued in favor of the more stringent standard. See Brown, 607 P.2d at 271-76 (Stewart, J., concurring in the judgment).
. Andrews relies heavily upon Hicks v. Oklahoma, 447 U.S. 343, 100 S.Ct. 2227, 65 L.Ed.2d 175 (1980). Hicks was convicted of distributing heroin and sentenced under an Oklahoma statute mandating a 40-year prison term for certain habitual offenders. The state appeals court noted that this provision had been declared unconstitutional before Hicks was tried, yet upheld the 40-year term because it fell within the range of punishment which a jury might have imposed. In holding that due process had been violated, the Supreme Court emphasized that Hicks was deprived of a specific statutory right to have a jury fix his sentence on "the frail conjecture” that the result might have been the same had he been afforded this right. See id. at 345-46, 100 S.Ct. at 2229. Andrews was deprived of no such entitlement under Utah law. Cf. Cabana v. Bullock, — U.S.-, 106 S.Ct. 689, 697 n. 4, 88 L.Ed.2d 704 (1986). In Andrews ni, the court considered whether he had a right to be resentenced under Wood and decided the question against him. Hicks is inapposite.
. The State mistakenly argues that Andrews did not preserve the claim that his sentence is excessive in light of the gravity of his offense because he did not intend that life would be taken. Although Enmund had yet to be decided, Andrews raised this issue on direct appeal and the Utah Supreme Court decided it. See Andrews II, 574 P.2d at 710-11; accord Andrews II, 607 P.2d at 818-20, 819 n. 9. The court again decided the merits of this issue on collateral attack in considering the retroactive applicability of Lockett v. Ohio, 438 U.S. 586, 98 S.Ct. 2954, 57 L.Ed.2d 973 (1978). See Andrews II, 607 P.2d at 824. Andrews’ Enmund claim may therefore be addressed.
. Instruction 13 provided in pertinent part:
"Once an individual indulges in planning or the assisting of criminal conduct he is responsible for the furtherance of that criminal conduct unless he has effectively withdrawn. In other words, if A and B plan a crime and A commits his assistance early in the crime, he would be responsible for B’s completion of the crime even if A had a change of heart during the commission of the crime unless he effectively withdrew____ In other words, if A and B have planned a crime together and after the beginning of the plan A has supplied some of the ware for the crime or rendered some service during the crime he is responsible for the completion of the crime even though he has had a change of heart, unless he destroys the effectiveness or withdraws the assistance he has given such as the supplying of tools for the crime so that his services or his part in conduct is not in fact an asset of the perpetrator of the crime."
Rec., vol. XVI, state trial rec., vol. R-3, at 358.
. Andrews also asserts that Utah’s provision for execution before a firing squad violates the Establishment Clause of the First Amendment, and that this method of execution constitutes cruel and unusual punishment in violation of the Eighth Amendment. Andrews failed to present his Establishment Clause claim in the state courts, which constitutes a default subject to the cause and prejudice test. We conclude that this challenge does not state a colorable claim. Accordingly, we need not inquire whether this test has been met. See Engle v. Isaac, 456 U.S. 107, 120 n. 19, 102 S.Ct. 1558, 1567 n. 19, 71 L.Ed.2d 783 (1982). In addition, we find no merit in Andrews’ Eighth Amendment claim. See Andrews IV, 600 F.Supp. at 431. Utah now allows defendants who have been sentenced to death to select either a firing squad or a lethal injection as the means of execution and mandates lethal injection if a defendant expresses no preference. See Utah Code Ann. § 77-18-5.5 (1986 Supp.).