On March 3,1974, after a jury trial in the Superior Court of Colquitt County, Georgia, appellant Willie X. Ross was convicted of armed robbery, kidnapping and murder. Sentences of life imprisonment, twenty years and the death penalty were imposed, respectively. The convictions and sentences were affirmed by the Georgia Supreme Court. Ross v. State, 233 Ga. 361, 211 S.E.2d 356 (1974), cert. denied, 428 U.S. 910, 96 S.Ct. 3222, 49 L.Ed.2d 1217 (1976). Ross petitioned for state habeas corpus relief, but, after a hearing, relief was denied. That decision was affirmed in Ross v. Hopper, 240 Ga. 369, 240 S.E.2d 850 (1977), cert. denied, 435 U.S. 1018, 98 S.Ct. 1890, 56 L.Ed.2d 397 (1978). Meanwhile, Ross filed a petition for declaratory judgment in the superior court, alleging that his trial jury was influenced by doubt as to the constitutional validity of the Georgia death penalty statute. The petition for declaratory judgment was denied, and the Georgia Supreme Court affirmed. Ross v. State, 238 Ga. 445, 233 S.E.2d 381 (1977).
Ross then filed a petition for federal habeas corpus relief in the United States District Court for the Southern District of Georgia. The matter was consolidated with two other cases in which the death penalty had been imposed, Mitchell v. Hopper, CV No. 478-132, and Spencer v. Zant, CV No. 179-247. The three petitions were denied. Mitchell v. Hopper, 538 F.Supp. 77 (S.D.Ga.1982); Ross v. Hopper, 538 F.Supp. 105 (S.D.Ga.1982). On appeal, a panel of this court affirmed in part the denial of Ross’ petition, but reversed and remanded for further evidentiary development on the issue of whether the Georgia death penalty statute was being applied arbitrarily and discriminatorily to blacks. Ross v. Hopper, 716 F.2d 1528 (11th Cir. 1983) . A majority of this court subsequently voted to rehear Ross’ appeal en banc, and the panel opinion was vacated. Ross v. Hopper, 729 F.2d 1293 (11th Cir. 1984) . On rehearing en banc, we again affirm in part the district court’s denial of Ross’ petition, but we remand to the panel for further consideration of Ross’ claim relating to the jury composition, in light of Ross’ motion to supplement the record.
I. The Facts1
On August 23, 1973, appellant Willie X. Ross, Freddie Lee King, Rudy Turner, and *1485Theodore Ross, appellant’s brother, drove from Madison, Florida to the Clover Farms Highway Grocery at Moultrie, Georgia. When the store closed for the evening they followed the individual who closed the store to a nearby house in which the J.R. Stanford family lived. They then drove back to Madison.
The next evening, August 24, the four men returned to the Stanford home. Wearing stocking masks over their faces, they entered the home, held the family at gunpoint and went through the house collecting various valuables, including Mr. Stanford’s .32 caliber pistol. Upon demanding the money from the grocery store, they were told it was in the possession of Robert Lee, who lived nearby, and that Wendell Norman, Stanford’s son-in-law and Lee’s partner in the grocery store, would return to the Stanford home later that night. When Norman arrived, he was ordered by the intruders to take Theodore Ross and King to get the money. Stanford’s fourteen-year-old stepdaughter was taken also as hostage. Appellant Willie Ross and Turner remained at the Stanford home.
Theodore Ross and King, with Norman and the stepdaughter, drove to Lee’s home, entered and proceeded to Lee’s bedroom. When Norman awoke Lee and explained why they were there, Lee reached for his pistol and fired into the hallway. Either Theodore Ross or King returned fire and grabbed one of Lee’s small sons, threatening to kill the child if Lee did not stop firing and turn over the money. Theodore Ross and King were given the cash box containing approximately $20,000 in cash and checks, and fled on foot. Norman then contacted the police.
Lieutenant Tommie Meredith of the Moultrie Police Department responded to the call and drove to the Stanford home, closely followed in a separate car by another officer. Members of the Stanford family testified that Meredith, armed with a shotgun, entered through the kitchen door confronting Turner, who, armed with a .22 caliber pistol, was crouching at the opposite end of a table in the adjoining dining room. Ross was seen standing against a wall near a refrigerator in the dining room and armed with Stanford’s .32 caliber pistol. Turner, stating, “Fve got them right here,” motioned for one of the family members to come toward him. The Stanfords, however, fled to a bedroom and closed the door. Immediately thereafter, both Mr. Stanford and the other police officer heard an exchange of gunfire. The officer, approaching the house from outside, saw and fired at two persons running from the house through the back yard.
The officer found Lieutenant Meredith’s body on the kitchen floor, shot through the chest at point-blank range. The pistol last seen in Turner’s possession was discovered in the back yard, fully loaded, the cartridge in the firing chamber bearing an indentation indicating the pistol had misfired. The .32 caliber pistol belonging to Stanford and last seen in Willie Ross’ hand seconds before the shooting, was found near the back-yard fence, one round having been fired from it. A microanalyst for the State Crime Laboratory identified the bullet removed from Meredith’s body as having been fired from the .32 caliber pistol.
Theodore Ross testified at appellant’s trial that appellant had told him that he (Willie Ross) thought he had shot a policeman and that Turner’s gun had misfired. Bobby Gamble, another prosecution witness, who had driven appellant back to Florida in the days subsequent to the incident, also testified that appellant had told him he thought he had killed a policeman.
Appellant was apprehended in New York several months after the incident, extradited to Georgia, and indicted for kidnapping, armed robbery, and murder. Appellant was convicted on all counts, and was sentenced to death for the murder of Lieutenant Meredith.
*1486II. The Claims
Appellant challenges the district court’s resolution of six of the issues raised in his federal habeas corpus petition. Appellant argues that (1) under the authority of Enmund v. Florida, 458 U.S. 782, 102 S.Ct. 3368, 73 L.Ed.2d 1140 (1982), the death penalty constitutionally may not be imposed when appellant was convicted of felony murder and there was no specific finding by the jury that he killed, attempted to kill, or intended to kill; (2) the precepts of Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), were violated by the state’s knowing use of perjured testimony of appellant’s brother Theodore that appellant had told Theodore he had shot a policeman; (3) the precepts of Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972), were violated by the state’s failure to disclose evidence contradicting Theodore’s statement that no promises had been made to him in exchange for his testimony against appellant; (4) the district court erroneously failed to hold an evidentiary hearing on appellant’s challenge to the composition of the grand and traverse juries;2 (5) an evidentiary hearing also was required in regard to appellant’s claim that the Georgia death penalty statute is applied in an arbitrary and racially discriminatory manner and with inadequate appellate review; and (6) the district court should have conducted an evidentiary hearing on appellant’s claim that failure to grant a change of venue due to prejudicial pretrial publicity deprived him of a fair trial. In addition, appellant contends for the first time on appeal that the charge to the jury in the sentencing phase of the trial did not adequately explain the function of mitigating circumstances, in violation of Spivey v. Zant, 661 F.2d 464 (5th Cir.1981), cert. denied, 458 U.S. 1111, 102 S.Ct. 3495, 73 L.Ed.2d 1374 (1982); Goodwin v. Balkcom, 684 F.2d 794 (11th Cir. 1982), cert. denied, 460 U.S. 1098,103 S.Ct. 1798, 76 L.Ed.2d 364 (1983); and West-brook v. Zant, 704 F.2d 1487 (11th Cir. 1983).
On rehearing en banc, we agree with the panel’s disposition of appellant’s Brady, Giglio, and change of venue claims, along with appellant’s challenge to the jury charge in the sentencing phase of the trial. We therefore reinstate sections II.B., II.C., II.F., and II.G. of the panel opinion. See Ross v. Hopper, 716 F.2d at 1533-37, 1539-42. We proceed to discuss appellant’s remaining claims.
A. The Enmund Claim
Appellant’s first remaining claim is based on Enmund v. Florida, 458 U.S. 782, 102 S.Ct. 3368, 73 L.Ed.2d 1140 (1982), where the Supreme Court held that the eighth amendment barred the imposition of the death penalty “in the absence of proof that [the defendant] killed or attempted to kill, and regardless of whether [he] intended or contemplated that life be taken____” Id. at 801, 102 S.Ct. at 3379. Appellant contends that Enmund’s, holding was violated in his case because the jury did not make a specific finding that he either murdered or intended to murder Lieutenant Meredith, and, therefore, he is entitled to a new sentencing hearing. Because we do not read Enmund as constitutionally requiring that a jury expressly make such a culpability determination, and because we find that the death penalty is proportional to appellant’s conduct under Enmund, we affirm the district court’s denial of habeas relief.
1.
In Enmund, the defendant was convicted and sentenced to death for murders committed by his co-felons during a robbery. The Florida Supreme Court affirmed the conviction and sentence on the theory that the jury could have found that En-mund drove the getaway car and was thus a principal responsible for his co-felons’ acts. Enmund v. State, 399 So.2d 1362, 1369-70 (Fla.1981). The Florida Supreme Court further concluded that, although the *1487evidence at most supported an inference that Enmund had driven the getaway car, there was no constitutional bar to imposing the death penalty even though the evidence did not show that the defendant intended that life be taken. Id. at 1371.
The United States Supreme Court reversed the defendant’s sentence, holding that the eighth amendment does not permit the imposition of the death penalty “on one such as Enmund who aids and abets a felony in the course of which a murder is committed by others but who does not himself kill, attempt to kill, or intend that a killing take place or that lethal force will be employed.” Enmund, 102 S.Ct. at 3376-77. The Court’s holding was based on the principle that a defendant’s sentence must not be grossly disproportionate to his crime. Id. at 3376 (“Petitioner’s argument is that because he did not kill, attempt to kill, and he did not intend to kill, the death penalty is disproportionate as applied to him____” (emphasis in original)).3 The Court also reasoned that the two principal social purposes of the death penalty — deterrence and retribution — would not be furthered by imposing the death penalty on a defendant who did not intend or contemplate that murder would take place. Deterrence would not be furthered because, quite simply, a person cannot be deterred who does not intend or contemplate that the acts being punished would occur. Id. at 3377-78. Similarly, retribution would not be justified where the punishment did not correspond with the defendant’s culpability — “what [his] intentions, expectations, and actions were,” id. at 3378, and where the defendant did not intend or cause the killings, the retributive purpose would not be served by executing the defendant. Therefore, because the record as construed by the Florida Supreme Court did “not warrant a finding that Enmund had any intention of participating in or facilitating a murder,” id. at 3377, the United States Supreme Court held that his sentence of death violated the eighth amendment.
2.
Although the Court in Enmund outlined a minimum threshold beneath which the defendant’s culpability must not fall if the death penalty is to be imposed, it did not delineate how or by whom the determination was to be made. Relying on cases holding that the question of the defendant’s guilt is solely for the jury, see, e.g., Bollenbach v. United States, 326 U.S. 607, 614, 66 S.Ct. 402, 614, 90 L.Ed. 350 (1946), appellant contends that the determination of whether the defendant’s culpability satisfies Enmund must be made by the jury and not by an appellate court from the record. Appellant notes that at least one other circuit has required that a new sentencing hearing be held where it is unclear from the jury’s verdict whether the jury found Enmund’s threshold of culpability satisfied. See Bullock v. Lucas, 743 F.2d 244 (5th Cir.1984), petition for cert. filed, 53 U.S.L.W. 3568 (U.S. Jan. 29, 1985) (No. 84-1236); Jones v. Thigpen, 741 F.2d 805 (5th Cir.1984), petition for cert. filed, 53 U.S.L.W. 3568 (U.S. Jan. 30, 1985) (No. 84-1237); Reddix v. Thigpen, 728 F.2d 705 (5th Cir.), reh’g denied, 732 F.2d 494 (5th Cir.1984), cert. denied, — U.S.-, 105 S.Ct. 397, 83 L.Ed.2d 331 (1984); see also Garcia v. Illinois, — U.S.-, 104 S.Ct. 3555, 82 L.Ed.2d 856 (1984) (Marshall, J., dissenting from denial of certiorari). But see State v. Tison, 142 Ariz. 446, 690 P.2d 747, 748-49 (1984) (en banc); People v. Garcia, 97 Ill.2d 58, 73 Ill.Dec. 414, 454 N.E.2d 274, 284-85 (1983), cert. denied, — U.S. -, 104 S.Ct. 3555, 82 L.Ed.2d 856 (1984).
*1488In our opinion, the question of whether the defendant’s culpability satisfies the eighth amendment is sufficiently distinct from the question of the defendant’s guilt that a specific jury finding is not constitutionally required. The necessity of ensuring that the jury finds every element of the crime beyond a reasonable doubt focuses on procedural due process concerns, see United States v. U.S. Gypsum Co., 438 U.S. 422, 98 S.Ct. 2864, 57 L.Ed.2d 854 (1978), whereas the proportionality review mandated by Enmund is aimed at ensuring that imposition of the death penalty is not excessive in light of the defendant’s culpability. 102 S.Ct. at 3377. We see no reason why the Enmund inquiry need be characterized as an additional element that the state must prove to the jury beyond a reasonable doubt at the guilt or sentencing phase before the death penalty lawfully can be imposed, so long as a reviewing court can determine from the record that the eighth amendment has been satisfied. It may very well be that a specific jury finding on the defendant’s intent or an “Enmund instruction” at the sentencing hearing is desirable, to develop a record that will assist a reviewing court in conducting a proper proportionality review in a particular case. We decline to transform the desirability of such procedures, however, into a constitutional requirement that the trier of fact make specific Enmund findings, such that every defendant sentenced to death without express jury findings on culpability is entitled to a new sentencing hearing.4
Thus, we conclude that specific jury findings on the defendant’s culpability are not a necessary constitutional corollary to the Court’s holding in Enmund. Consequently, appellant is not entitled to a new sentencing hearing in this case solely because his jury returned a general guilty verdict after being instructed on felony murder and conspiracy. Rather, just as the Supreme Court in Enmund reviewed the record as construed by the Florida Supreme Court, we also must turn to the record to determine whether appellant’s sentence violates the eighth amendment.5
3.
In Enmund, the Supreme Court reversed the defendant’s death penalty because it had been imposed “in the absence of proof that Enmund killed or attempted to kill, and regardless of whether Enmund intended or contemplated that life be taken____” 102 S.Ct. at 3379 (emphasis supplied). Appellant’s involvement in this case stands in stark contrast to Enmund’s role as the driver of a getaway car. Even taking all of the evidence most favorably to appellant, we conclude that his culpability as shown by the record satisfies the eighth amendment standard set out in Enmund.
Although the jury was charged on felony murder, the state’s theory at trial was that appellant was the triggerman. Testimony showed that, when Lieutenant Meredith entered the house, appellant was positioned in the dining room and armed with a .32 caliber pistol stolen from Stanford. Turner was also armed with a pistol, crouched at *1489the end of the dining room table away from the kitchen. Witnesses heard two shots from Meredith’s shotgun, followed by a single pistol shot. Turner and appellant fled through the backyard while being fired upon by Officer Lynch, who had arrived shortly after Lieutenant Meredith. Two guns were later found in the backyard: Turner’s pistol, which was fully loaded and had a cartridge in the firing chamber that was indented, indicating it had misfired, and the .32 caliber pistol, last seen in appellant’s possession, which ballistic tests later showed had fired the shot that killed Meredith. At trial, appellant’s brother testified that appellant had told him that he had shot a policeman and that Turner’s gun had misfired. Another witness also testified that appellant had stated that he thought he had killed a policeman.
The above summary of the evidence presented at trial, as recounted by the Georgia Supreme Court, Ross v. State, 233 Ga. 361, 364, 211 S.E.2d 356, 358 (1974), would fully warrant a conclusion that appellant fired the shot that killed Lieutenant Meredith. Appellant, however, suggests that the possibility exists that Turner, upon having his pistol misfire, may have grabbed the .32 caliber pistol and fired the fatal shot instead of appellant. Appellant also relies on his brother’s later recantation of his testimony that appellant had told him that he had shot a policeman. Even accepting appellant’s rather strained version of events and the remote possibility that appellant did not himself fire the fatal shot, we believe that the uncontroverted evidence in the record shows that appellant’s sentence of death does not violate the eighth amendment.
We do not read Enmund as barring the death penalty for all non-triggermen, but merely as requiring a level of individual participation that justifies the application of the death penalty. 102 S.Ct. at 3377. The Supreme Court’s objection in Enmund that Earl Enmund was to be executed “regardless of whether [he] intended or contemplated that life would be taken,” id. at 3379, simply does not extend to appellant, whose actions undeniably reflect the contemplation that life would be taken. Appellant does not deny that he and Turner held the Stanford family hostage while their cohorts went to the Lee home. Likewise, it is undisputed that appellant was armed and in the dining room with Turner when Lieutenant Meredith entered the home. He was thus actively engaged in furthering the course of events that led directly to Meredith’s murder, whether or not he actually pulled the trigger.
More fundamentally, it is evident that the two primary purposes of capital punishment — deterrence and retribution — legitimately can be applied to the facts of this case. The Enmund Court observed that the death penalty will not likely deter “if a person does not intend that life be taken or contemplate that lethal force will be employed by others____” Id. at 3377. Here, however, it would be incredible to believe that appellant did not contemplate that lethal force would be used either by himself or his accomplice. Likewise, the “intentions, expectations, and actions,” id. at 3378, of an individual engaging in such acts rise to a level of culpability such that the retributive purposes of capital punishment are furthered by appellant’s sentence of death.
In sum, even if appellant’s actions are viewed in their most favorable light, and even if we completely discount the testimony of those witnesses who stated that appellant had told them he thought he had shot a policeman, appellant’s culpability still is of a magnitude wholly different from that of Earl Enmund. In Enmund, the evidence showed at most that the defendant had been seated in a getaway car at the side of the road awaiting the robbers’ escape. In contrast, the record here depicts an individual who undoubtedly contemplated that lethal force would be used either by himself or by others as they held a family hostage, and who actively participated in the activities that culminated in Lieutenant Meredith’s death. Consequently, we find that the death penalty in this case does not violate the eighth amendment, and we affirm the district court’s *1490denial of habeas corpus relief on this ground.
B. The Jury Composition Claim
Appellant’s next claim is that the venires from which the grand and traverse juries that indicted, convicted and sentenced him were selected, substantially underrepresented blacks and women. The district court rejected this claim because appellant “was afforded a full and fair opportunity to present his jury composition issue to the courts of Georgia and ... simply failed to meet his burden of proof.” Ross v. Hopper, 538 F.Supp. at 106. The district court therefore applied the presumption of correctness created by 28 U.S.C. § 2254(d) to the state courts’ determination that appellant’s claim had no factual basis. Id. The panel affirmed, noting that appellant did not establish that his claim fell within one of the exceptions to the statutory presumption of correctness listed in Townsend v. Sain, 372 U.S. 293, 83 S.Ct. 745, 9 L.Ed.2d 770 (1963). See Ross v. Hopper, 716 F.2d at 1537-39.
On the same day this court reheard the instant case en banc, appellant filed a motion to supplement the record concerning his jury composition claim. Because the evidence now proffered by appellant may affect the applicability of one or more of the Townsend exceptions, we remand to the panel for consideration of this claim in light of appellant’s motion to supplement the record.
C. The Arbitrary and Racially Discriminatory Application Claim
Appellant’s final claim is that the Georgia death penalty statute is applied in an arbitrary and racially discriminatory manner and with inadequate appellate review. Appellant first raised this claim in his state habeas corpus petition in 1976.6 At an evidentiary hearing on December 9, 1976, appellant introduced testimony by Dr. Tobe Johnson, a professor of political science at Morehouse College. Dr. Johnson testified concerning his review of two social science studies on racial discrimination in the application of the death penalty in Georgia.7 On March 22, 1977, the superior court denied appellant’s habeas petition. Appellant moved to reopen the evidentiary hearing in order to introduce a 1972 study of capital punishment in Georgia conducted by the Georgia Department of Corrections. The motion was denied.
The Georgia Supreme Court affirmed the superior court’s denial of habeas relief. Ross v. Hopper, 240 Ga. 369, 240 S.E.2d 850 (1977), cert. denied, 435 U.S. 1018, 98 S.Ct. 1890, 56 L.Ed.2d 397 (1978). The court noted that “[Dr. Johnson’s] testimony was largely based on his analysis of data gathered prior to the decision in Furman v. Georgia, 408 U.S. 238 [92 S.Ct. 2726, 33 L.Ed.2d 346] (1972),” and that the Georgia Department of Corrections study “was based on a study of capital punishment in Georgia for the years 1943 to 1965” and therefore was “irrelevant to this case since [Ross] was convicted and sentenced after Furman v. Georgia.” Ross, 240 S.E.2d at 852-53. The court concluded that appellant’s evidence “was insufficient to show that the death penalty was arbitrarily and capriciously imposed in his case as a result of deliberate discrimination____” Id. at 853.
Appellant also asserted the claim in his federal habeas corpus petition in 1978. Appellant’s petition was consolidated with those of two other petitioners, James Lee Spencer and William “Billy” Mitchell, both of whom raised the same claim. At a hearing on January 26, 1981, counsel for all three petitioners proffered a study, conducted by Dr. William Bowers and Glenn Pierce, of criminal homicides and the death penalty in Georgia and other states be*1491tween July, 1972, and August, 1980 (the “Bowers and Pierce study”).8 Counsel also proffered a study, conducted by University of Texas law professor George Dix, of appellate review in cases where the death penalty was imposed (the “Dix study”).9 The district court denied counsel’s request for an evidentiary hearing to introduce the proffered studies.
On April 6, 1982, the court entered final judgment denying the three consolidated petitions. Mitchell v. Hopper, 538 F.Supp. 77 (S.D.Ga.1982); Ross v. Hopper, 538 F.Supp. 105 (S.D.Ga.1982). On April 15, appellant filed a memorandum of law in support of a motion to alter or amend the judgment of the court. In the memorandum of law, appellant proffered a study, conducted by Dr. David C. Baldus, of the application of the death penalty in Georgia (the “Baldus study”).10 The motion to alter or amend the judgment was denied.
On appeal from the denial of Spencer’s petition, a panel of this court held, inter alia, that the district court erred in refusing counsel’s request for an evidentiary hearing to introduce the Baldus study. Spencer v. Zant, 715 F.2d 1562, 1578-83 (11th Cir.), en banc reh’g granted, 715 F.2d 1583 (11th Cir.1983), decision withheld pending submission and en banc consideration of McCleskey v. Zant and Ross v. Hopper, 729 F.2d 1293, 1294 (11th Cir. 1984). The panel therefore vacated the judgment and remanded for an evidentiary hearing. Spencer v. Zant, 715 F.2d at 1583. On appeal from the denial of Ross’ petition, the same panel, relying on Spencer v. Zant, reversed and remanded “for further evidentiary development” as to the arbitrary and racially discriminatory application claim. Ross v. Hopper, 716 F.2d 1528, 1539 (11th Cir.1983), en banc reh’g granted, 729 F.2d 1293, 1294 (11th Cir. 1984).
Upon reevaluation of appellant’s claim in light of our recent en banc opinion in McCleskey v. Kemp, 753 F.2d 877 (11th Cir.1985), we hold that the district court did not err when it denied appellant’s request for an evidentiary hearing. In McCleskey, we explained that statistical evidence of a disparate impact in the imposition of the death penalty is relevant only to the extent that it compels an inference of purposeful discrimination:
[Pjroof 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.
Id. at 892.
Hence, when a petitioner proffers statistical evidence of the kind relied upon by appellant in the instant case, the district court need not hold an evidentiary hearing unless the proffer demonstrates a reasonable possibility that the evidence might compel an inference of purposeful discrimination. As we stated in McCleskey:
Needless to say, an evidentiary hearing would be necessary to hear any evidence that a particular defendant was discriminated against because of his race. But general statistical studies of the kind offered here do not even purport to prove that fact. Aside from that kind of evidence, however, it would not seem necessary to conduct a full evidentiary hearing as to studies which do nothing more than show an unexplainable disparity. Generalized studies would appear to have little hope of excluding ev*1492ery possible factor that might make a difference between crimes and defendants, exclusive of race. To the extent there is a subjective or judgmental component to the discretion with which a sentence is invested, not only will no two defendants be seen identical by the sentencers, but no two sentencers will see a single case precisely the same. As the court has recognized, there are “countless racially neutral variables” in the sentencing of capital cases. Smith v. Balkcom, 671 F.2d [858,] 859 [(5th Cir. Unit B), cert. denied, 459 U.S. 882, 103 S.Ct. 181, 74 L.Ed.2d 148 (1982) ].
Id. at 894 (emphasis added).11
The proffer in the instant case falls far short of demonstrating a reasonable possibility that the evidence might compel such an inference. With respect to the studies raised in the. state habeas corpus proceedings, we agree with the Georgia Supreme Court that, because those studies were based on data gathered prior to Furman v. Georgia, they do not support appellant’s claim. Statistical evidence of disparate impact in the pre-Furman Georgia capital sentencing system can hardly compel an inference of purposeful discrimination in the post-Furman system.
With respect to the Baldus study, McCleskey is squarely controlling. Because the district court in McCleskey held an extensive evidentiary hearing on the Baldus study, this court had the opportunity to consider, on the basis of a fully developed record, both the methodology of the study and the inferences to be drawn from it. We discussed the strengths and weaknesses of statistical evidence in general, and the Baldus study in particular, before concluding that “the Baldus study is simply insufficient to support a ruling, in the context of a statute that is operating much as intended, that racial factors are playing a role in the outcome sufficient to render the system as a whole arbitrary and capricious.” McCleskey, 753 F.2d at 897. We therefore held that, even assuming the validity of the Baldus study’s methodology, “the statistics are inadequate to entitle McCleskey to relief on his constitutional claim.” Id. at 896. Our holding in McCles-key forecloses any possible reliance on the Baldus study in the instant case, and appellant is not entitled to an evidentiary hearing on the Baldus study.
With respect to the Bowers and Pierce study, we conclude that appellant’s proffer fails to demonstrate a reasonable possibility that the study might compel an inference of purposeful discrimination. The Bowers and Pierce study purported to show a disparity in the imposition of the death penalty in Georgia and other states, based on race, between July, 1972 and August, 1980. Unlike the Baldus study, however, the Bowers and Pierce study did not attempt “to control for all of the factors which play into a capital crime system.” Id. at 887. In fact, the only factor controlled for in the Bowers and Pierce study was whether the homicide was a felony murder or non-felony murder. See Bowers & Pierce, Arbitrariness and Discrimination under Post-Furman Capital Statutes, 26 Crime & Delinq. 563, 597-600 & Table 3 (1980). On this basis alone, we find the Bowers and Pierce study legally insufficient to compel an inference of purposeful discrimination in the imposition of the death penalty.
In addition, we note that the same Bowers and Pierce study was proffered in Smith v. Balkcom, 671 F.2d 858, 859 (5th Cir. Unit B 1982). There, a panel of this court identified problems with the study that east serious doubt on its overall validity. The Smith v. Balkcom panel stated:
Appellant’s statistician sought to determine the total number of incidents involving homicide reported as having taken place in Georgia by a somewhat arbitrary (but accepted as statistically *1493correct) adjustment for unreported incidents. He used Supplemental Homicide Reports (SHRs) submitted by Georgia law enforcement officers to the Federal Bureau of Investigation. (He compiled a supplemental data base of those homicides associated with the commission of some other felony — one, but only one, of the aggravating circumstances under the statute____) The study then compares these reported incidents with death penalties ultimately imposed, after trial, in the state. No data is offered as to whether or not charges or indictments grew out of reported incidents or as to whether charges were for murder under aggravating circumstances, murder in which no aggravating circumstances were alleged, voluntary manslaughter, involuntary manslaughter, or other offenses. The data are not refined to select incidents in which mitigating circumstances were advanced or found or those cases in which evidence of aggravating circumstances was sufficient to warrant submission of the death penalty vel non to a jury. No incidents resulting in not guilty verdicts were removed from the data. The unsupported assumption is that all such variables were equally distributed, racially, sexually, offender and victim, throughout the SHRs. No conclusions of evidentiary value can be predicated upon such unsupported assumptions.
671 F.2d at 860 n. 33 (citations omitted). In short, the Bowers and Pierce study shares none of the characteristics that made the Baldus study worthy of extensive judicial scrutiny. Because appellant failed to demonstrate a reasonable possibility that the Bowers and Pierce study might compel an inference of purposeful discrimination in the imposition of the death penalty, we hold that appellant is not entitled to an evidentiary hearing on the Bowers and Pierce study.12
Finally, with respect to the Dix study, appellant proffered the study solely forth e purpose of demonstrating that the Georgia Supreme Court’s appellate review of death penalty cases does not eliminate the alleged arbitrariness and racial discrimination in the Georgia capital sentencing system. The appellant did not claim, nor could he have claimed, that the Dix study showed that appellate review produced discrimination or increased the level of discrimination in the system.13 In the absence of independent, credible evidence of purposeful discrimination, we find it irrelevant whether or not the Georgia Supreme Court’s appellate review procedure is adequate to eliminate such discrimination. We hold that the Dix study, standing alone, does not provide a basis for habeas corpus relief, and appellant is not entitled to an evidentiary hearing on the Dix study.
In conclusion, appellant has failed to proffer any evidence that might compel an inference of purposeful discrimination in the imposition of the death penalty in Georgia. We therefore affirm the district court’s denial of appellant’s request for an *1494evidentiary hearing as to the arbitrary and racially discriminatory application claim.
III. Conclusion
Based on the foregoing discussion, we hereby AFFIRM in part the district court’s denial of Ross’ petition, but we REMAND to the panel for further consideration Ross’ claim relating to the jury composition, in light of Ross’ motion to supplement the record.
. The statement of the facts is adapted from the panel opinion, Ross v. Hopper, 716 F.2d at 1530-*148531, and is substantially similar to that of the Georgia Supreme Court in Ross' v. State, 211 S.E.2d at 357-58.
. Appellant’s challenge to the jury venires potentially would affect all of the convictions. It appears, however, that appellant challenges only the murder conviction and the imposition of the death penalty.
. The Supreme Court’s most recent proportionality decision, Solem v. Helm, 463 U.S. 277, 103 S.Ct. 3001, 77 L.Ed.2d 637 (1983), confirms that Enmund was indeed a proportionality case. The Solem Court described Enmund as a case in which "the Court ... applied the principle of proportionality to hold capital punishment excessive in certain circumstances.” Solem, 103 S.Ct. at 3008; see also Pulley v. Harris, 465 U.S. 37, 104 S.Ct. 871, 875, 79 L.Ed.2d 29, 35 (1984) (citing both Solem and Enmund as examples of proportionality cases). In addition, the Solem Court repeatedly turned to Enmund for guidance concerning how to conduct a proper proportionality review. See Solem, 103 S.Ct. at 3010-11.
. Even if we were to adopt appellant's argument, we would find that the absence of such findings here constituted harmless error, as the overwhelming evidence shows that appellant’s conduct demonstrated sufficient culpability to satisfy the eighth amendment. Although in Connecticut v. Johnson, 460 U.S. 73, 103 S.Ct. 969, 74 L.Ed.2d 823 (1983), the Supreme Court evenly divided over whether a conclusive presumption that took the issue of intent away from the jury could be harmless error, this court has held that such instructions can constitute harmless error. Lamb v. Jernigan, 683 F.2d 1332, 1342 (11th Cir.1982), cert. denied, 460 U.S. 1024, 103 S.Ct. 1276, 75 L.Ed.2d 496 (1983).
. Judge Clark, in dissent, contends that our decision today "arrogates to the federal courts in habeas corpus cases the authority to conduct a case by case proportionality review in death cases, an authority we do not have.” Post at 1487. We find support for our position in Solem v. Helm, 463 U.S. 277, 103 S.Ct. 3001, 77 L.Ed.2d 637 (1983), a habeas corpus case in which the Supreme Court conducted an extensive proportionality review based on the facts of the case. We see no reason to conclude that federal courts can conduct such a proportionality review in non-death penalty habeas corpus cases like Solem, but not in death penalty cases, where the stakes are so much higher.
. At the same time, appellant filed a "Motion for Appointment of Experts, Authorization of Investigation and Continuance,” requesting a state-supported factual investigation of his claim. The motion was denied.
. Wolfgang & Riedel, Race, Judicial Discretion and the Death Penalty, 407 Annals 119 (1973); Wolfgang & Riedel, Race, Rape and the Death Penalty in Georgia, 45 Am.J.Ortho. 658 (1975).
. The Bowers and Pierce study was reported in an article entitled "Arbitrariness and Discrimination under Post-Furman Capital Statutes,” which appeáred at 26 Crime & Delinq. 563 (1980).
. The Dix study was reported in an article entitled "Appellate Review of the Decision to Impose Death," which appeared at 68 Geo.L.J. 97 (1979).
. See Baldus, Identifying Comparatively Excessive Sentences of Death: A Quantitative Approach, 33 Stan.L.Rev. 1 (1980).
. We also cautioned in McCleskey, however, that "statistical studies may reflect a disparity so great as to inevitably lead to a conclusion that the disparity results from intent or motivation.” Id. at 894. Furthermore, at least arguably, “the proof of racial motivation required in a death case ... would be less strict than that required in civil cases or in the criminal justice system generally." Id. at 905-07 (Anderson and Krav-itch, JJ., concurring).
. The Bowers and Pierce study also purported to show that the death penalty is arbitrarily imposed on the basis of geographic location within each particular state. See Bowers & Pierce, Arbitrariness and Discrimination under Post-Furman Capital Statutes, 26 Crime & Del-inq. 563, 601-607 & Tables 4-6. The study divided the total number of homicides in Georgia into geographical "regions,” including North Georgia, Central Georgia, Southwest Georgia, Southeast Georgia, and Fulton County, and compared the probability of receiving the death penalty in each of these regions. As in the case of race, however, the study did not attempt to control for any factors other than whether the homicide was a felony murder or a non-felony murder. Therefore, we conclude that the study is legally insufficient to compel an inference of arbitrariness in the imposition of the death penalty based on location.
. The Dix study did not even discuss arbitrariness or discrimination in the Georgia capital sentencing system as a whole. Rather, the Dix study evaluated the performance of the Georgia Supreme Court in death penalty cases by reviewing the court’s reported opinions. The only statistical evidence in the study relating to Georgia is a numerical table showing the disposition of death penalty cases in the Georgia Supreme Court. See Dix, Appellate Review of the Decision to Impose Death, 68 Geo.LJ. 97, 111 & Table 1 (1979).