with whom Judges TJOFLAT, JAMES C. HILL, FAY, VANCE, ALBERT J. HENDERSON and R. LANIER ANDERSON, III, join *:
This case was taken en banc principally to consider the argument arising in numerous capital cases that statistical proof shows the Georgia capital sentencing law is being administered in an unconstitutionally discriminatory and arbitrary and capricious matter. After a lengthy evidentiary hearing which focused on a study by Professor David C. Baldus, the district court concluded for a variety of reasons that the statistical evidence was insufficient to support the claim of unconstitutionality in the death sentencing process in Georgia. We affirm the district court’s judgment on this point.
The en banc court has considered all the other claims involved on this appeal. On the State’s appeal, we reverse the district court’s grant of habeas corpus relief on the claim that the prosecutor failed to disclose a promise of favorable treatment to a state witness in violation of Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972). We affirm the judgment denying relief on all other points raised by the defendant, that is: (1) that defendant received ineffective assistance of *882counsel; (2) that jury instructions contravened the due process clause in violation of Sandstrom v. Montana, 442 U.S. 510, 99 S.Ct. 2450, 61 L.Ed.2d 39 (1979); and (3) that the exclusion of death-scrupled jurors violated the right to an impartial and unbiased jury drawn from a representative cross-section of the community.
Thus, concluding that the district court should have denied the petition for writ of habeas corpus, we affirm on all claims denied by the court, but reverse the grant of habeas corpus relief on the Giglio claims.
FACTS
Warren MeCleskey was arrested and charged with the murder of a police officer during an armed robbery of the Dixie Furniture Store. The store was robbed by a band of four men. Three entered through the back door and one through the front. While the men in the rear of the store searched for cash, the man who entered through the front door secured the showroom by forcing everyone there to lie face down on the floor., Responding to a silent alarm, a police officer entered the store by the front door. Two shots were fired. One shot struck the police officer in the head causing his death. The other glanced off a cigarette lighter in his chest pocket.
MeCleskey was identified by two of the store personnel as the robber who came in the front door. Shortly after his arrest, MeCleskey confessed to participating in the robbery but maintained that he was not the triggerman. MeCleskey confirmed the eyewitness’ accounts that it was he who entered through the front door. One of his accomplices, Ben Wright, testified that MeCleskey admitted to shooting the officer. A jail inmate housed near MeCleskey testified that MeCleskey made a “jail house confession” in which he claimed he was the triggerman. The police officer was killed by a bullet fired from a .38 caliber Rossi handgun. MeCleskey had stolen a .38 caliber Rossi in a previous holdup.
PRIOR PROCEEDINGS
The jury convicted MeCleskey of murder and two counts of armed robbery. At the penalty hearing, neither side called any witnesses. The State introduced documentary evidence of McCleskey’s three prior convictions for armed robbery.
The jury sentenced MeCleskey to death for the murder of the police officer and to consecutive life sentences for the two counts of armed robbery. These convictions and sentences were affirmed by the Georgia Supreme Court. McClesky v. State, 245 Ga. 108, 263 S.E.2d 146, cert. denied, 449 U.S. 891, 101 S.Ct. 253, 66 L.Ed.2d 119 (1980). MeCleskey then petitioned for habeas corpus relief in state court. This petition was denied after an evidentiary hearing. The Georgia Supreme Court denied McCleskey’s application for a certificate of probable cause to appeal. The United States Supreme Court denied a petition for a writ of certiorari. MeCleskey v. Zant, 454 U.S. 1093, 102 S.Ct. 659, 70 L.Ed.2d 631 (1981).
MeCleskey then filed his petition for ha-beas corpus relief in federal district court asserting, among other things, the five constitutional challenges at issue on this appeal. After an evidentiary hearing and consideration of extensive memoranda filed by the parties, the district court entered the lengthy and detailed judgment from which these appeals are taken. MeCleskey v. Zant, 580 F.Supp. 338 (N.D.Ga.1984).
This opinion addresses each issue asserted on appeal in the following order: (1) the Giglio claim, (2) constitutionality of the application of Georgia’s death penalty, (3) effective assistance of counsel, (4) death-qualification of jurors, and (5) the Sand-strom issue.
GIGLIO CLAIM
The district court granted habeas corpus relief to MeCleskey because it determined that the state prosecutor failed to reveal that one of its witnesses had been promised favorable treatment as a reward for his testimony. The State violates due process when it obtains a conviction through the use of false evidence or on the *883basis of a witness’s testimony when that witness has failed to disclose a promise of favorable treatment from the prosecution. Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972).
We hold that (1) there was no promise in this case, as contemplated by Giglio; and (2) in any event, had there been a Giglio violation, it would be harmless. Thus, we reverse the grant of habeas corpus relief on this ground.
Offie Gene Evans, a prisoner incarcerated with McCleskey, was called by the State on rebuttal to strengthen its proof that McCleskey was the triggerman at the holdup. Evans testified that McCleskey admitted to him in jail that he shot the policeman and that McCleskey said he had worn makeup to disguise his appearance during the robbery.
The “Promise ”
At McCleskey’s state habeas corpus hearing, Evans gave the following account of certain conversations with state officials.
THE COURT: Mr. Evans, let me ask you a question. At the time that you testified in Mr. McCleskey’s trial, had you been promised anything in exchange for your testimony?
THE WITNESS: No, I wasn’t. I wasn’t promised nothing about — I wasn’t promised nothing by the D.A. but the Detective told me that he would — he said he was going to do it himself, speak a word for me. That was what the Detective told me.
Q: (by McCleskey’s attorney): The Detective said he would speak a word for you?
A: Yeah.
A deposition of McCleskey’s prosecutor that was taken for the state habeas corpus proceeding reveals that the prosecutor contacted federal authorities after McCles-key’s trial to advise them of Evans’ cooperation and that the escape charges were dropped.
The Trial Testimony
At the trial, the State brought out on direct examination that Evans was incarcerated on the charge of escape from a federal halfway house. Evans denied receiving any promises from the prosecutor and downplayed the seriousness of the escape charge.
Q: [by prosecutor]: Mr. Evans, have I promised you anything for testifying today?
A: No, sir, you ain’t.
Q: You do have an escape charge still pending, is that correct?
A: Yes, sir. I’ve got one, but really it ain’t no escape, what the peoples out there tell me, because something went wrong out there so I just went home. I stayed at home and when I called the man and told him that I would be a little late coming in, he placed me on escape charge and told me there wasn’t no use of me coming back, and I just stayed on at home and he come and picked me up.
Q: Are you hoping that perhaps you won’t be prosecuted for that escape?
A: Yeah, I hope I don’t, but I don’t— what they tell me, they ain’t going to charge me with escape no way.
Q: Have you asked me to try to fix it so you wouldn’t get charged with escape?
A: No, sir.
Q: Have I told you I would try to fix it for you?
A: No, sir.
The State Habeas Corpus Decision
The state court rejected McCleskey’s Giglio claim on the following reasoning:
Mr. Evans at the habeas hearing denied that he was promised anything for his testimony. He did state that he was told by Detective Dorsey that Dorsey would ‘speak a word’ for him. The detective’s ex parte communication recommendation alone is not sufficient to trigger the applicability of Giglio v. United States, 405 U.S. 150 [92 S.Ct. 763, 31 L.Ed.2d 104] (1972).
*884The prosecutor at petitioner’s trial, Russel J. Parker, stated that he was unaware of any understandings between Evans and any Atlanta Police Department detectives regarding a favorable recommendation to be made on Evans’ federal escape charge. Mr. Parker admitted that there was opportunity for Atlanta detectives to put in a good word for Evans with federal authorities. However, he further stated that when any police officer has been killed and someone ends up testifying for the State, putting his life in danger, it is not surprising that charges, like those against Evans, will be dropped.
In the absence of any other evidence, the Court cannot conclude an agreement existed merely because of the subsequent disposition of criminal charges against a witness for the State.
Although it is reasonable to conclude that the state court found that there was no agreement between Evans and the prosecutor, no specific finding was made as to Evans’ claim that a detective promised to “speak a word for him.” The court merely held as a matter of law that assuming Evans was telling the truth, no Giglio violation had occurred.
Was It a Promise?
The Supreme Court’s rationale for imposing this rule is that “[t]he jury’s estimate of the truthfulness and reliability of a given witness may well be determinative of guilt or innocence.” Napue v. Illinois, 360 U.S. 264, 269, 79 S.Ct. 1173, 1177, 3 L.Ed.2d 1217 (1959). The Court has never provided definitive guidance on when the Government’s dealings with a prospective witness so affect the witness’ credibility that they must be disclosed at trial. In Giglio, a prosecutor promised the defendant’s alleged co-conspirator that no charges would be brought against him if he testified against the defendant. In Napue, a prosecutor promised a witness that in exchange for his testimony the prosecutor would recommend that the sentence the witness was presently serving be reduced.
In this case, the detective’s promise to speak a word falls far short of the understandings reached in Giglio and Napue. As stated by this Court, “[t]he thrust of Giglio and its progeny has been to ensure that the jury know the facts that might motivate a witness in giving testimony.” Smith v. Kemp, 715 F.2d 1459, 1467 (11th Cir.), cert. denied, — U.S.—, 104 S.Ct. 510, 78 L.Ed.2d 699 (1983). The detective’s statement offered such a marginal benefit, as indicated by Evans, that it is doubtful it would motivate a reluctant witness, or that disclosure of the statement would have had any effect on his credibility. The State’s nondisclosure therefore failed to infringe McCleskey’s due process rights.
Was Any Violation Harmless?
In any event, there is no “reasonable likelihood” that the State’s failure to disclose the detective’s cryptic statement or Evans’ different escape scenario affected the judgment of the jury. See Giglio, 405 U.S. at 154, 92 S.Ct. at 766. Evans’ credibility was exposed to substantial impeachment even without the detective’s statement and the inconsistent description of his escape. The prosecutor began his direct examination by having Evans recite a litany of past convictions. Evans admitted to convictions for forgery, two burglaries, larceny, carrying a concealed weapon, and theft from the United States mail. On cross examination, McCleskey’s attorney attempted to portray Evans as a “professional criminal”. Evans also admitted that he was testifying to protect himself and one of McCleskey’s codefendants. In light of this substantial impeachment evidence, we find it unlikely that the undisclosed information would have affected the jury’s assessment of Evans’ credibility. See United States v. Anderson, 574 F.2d 1347, 1356 (5th Cir.1978).
McCleskey claims Evans’ testimony was crucial because the only other testimony which indicated he pulled the trigger came from his codefendant, Ben Wright. Ben Wright’s testimony, McCleskey urges, *885would have been insufficient under Georgia law to convict him without the corroboration provided by Evans. In Georgia, an accomplice’s testimony alone in felony cases is insufficient to establish a fact. O.C.G.A. § 24-4-8. Wright’s testimony, however, was corroborated by McCleskey’s own confession in which McCleskey admitted participation in the robbery. See Arnold v. State, 236 Ga. 534, 224 S.E.2d 386, 388 (1976). Corroboration need not extend to every material detail. Blalock v. State, 250 Ga. 441, 298 S.E.2d 477, 479-80 (1983); Cofer v. State, 166 Ga.App. 436, 304 S.E.2d 537, 539 (1983).
The district court thought Evans’ testimony critical because of the information he supplied about makeup and McCleskey’s intent in shooting the police officer. Although we agree that his testimony added weight to the prosecution’s case, we do not find that it could “in any reasonable likelihood have affected the judgment of the jury.” Giglio, 405 U.S. at 154, 92 S.Ct. at 766 (quoting Napue v. Illinois, 360 U.S. at 271, 79 S.Ct. at 1178). Evans, who was called only in rebuttal, testified that McCleskey had told him that he knew he had to shoot his way out, and that even if there had been twelve policemen he would have done the same thing. This statement, the prosecutor argued, showed malice. In his closing argument, however, the prosecutor presented to the jury three reasons supporting a conviction for malice murder. First, he argued that the physical evidence showed malicious intent because it indicated that McCleskey shot the police officer once in the head and a second time in the chest as he lay dying on the floor. Second, the prosecutor asserted that McCleskey had a choice, either to surrender or to kill the officer. That he chose to kill indicated malice. Third, the prosecutor contended that McCleskey’s statement to Evans that he still would have shot his way out if there had been twelve police officers showed malice. This statement by McCles-key was not developed at length during Evans’ testimony and was mentioned only in passing by the prosecutor in closing argument.
Evans’ testimony that McCleskey had made up his face corroborated the identification testimony of one of the eyewitnesses. Nevertheless, this evidence was not crucial to the State’s case. That McCles-key was wearing makeup helps to establish he was the robber who entered the furniture store through the front door. This fact had already been directly testified to by McCleskey’s accomplice and two eyewitnesses as well as corroborated by McCles-key’s own confession. That Evans’ testimony buttresses one of the eyewitnesses’ identifications is relatively unimportant.
Thus, although Evans’ testimony might well be regarded as important in certain respects, the corroboration of that testimony was such that the revelation of the Giglio promise would not reasonably affect the jury’s assessment of his credibility and therefore would have had no effect on the jury’s decision. The district court’s grant' of habeas corpus relief on this issue must be reversed.
CONSTITUTIONAL APPLICATION OF GEORGIA’S DEATH PENALTY
In challenging the constitutionality of the application of Georgia’s capital statute, McCleskey alleged two related grounds for relief: (1) that the “death penalty is administered arbitrarily, capriciously, and whimsically in the State of Georgia,” and (2) it “is imposed ... pursuant to a pattern and practice ... to discriminate on the grounds of race,” both in violation of the Eighth and Fourteenth Amendments of the Constitution.
The district court granted petitioner’s motion for an evidentiary hearing on his claim of system-wide racial discrimination under the Equal Protection Clause of the Fourteenth Amendment. The court noted that “it appears ... that petitioner’s Eighth Amendment argument has been rejected by this Circuit in Spinkellink v. Wainwright, 578 F.2d 582, 612-14 (5th Cir.1978) ... [but] petitioner’s Fourteenth Amendment claim may be appropriate for consideration in the context of statistical *886evidence which the petitioner proposes to present.” Order of October 8, 1982, at 4.
An evidentiary hearing was held in August, 1983. Petitioner's case in chief was presented through the testimony of two expert witnesses, Professor David C. Bal-dus and Dr. George Woodworth, as well as two principal lay witnesses, Edward Gates and L.G. Warr, an official employed by Georgia Board of Pardons and Paroles. The state offered the testimony of two expert witnesses, Dr. Joseph Katz and Dr. Roger Burford. In rebuttal, petitioner recalled Professor Baldus and Dr. Wood-worth, and presented further expert testimony from Dr. Richard Berk.
In a comprehensive opinion, reported at 580 F.Supp. 338, the district court concluded that petitioner failed to make out a prima facie case of discrimination in sentencing based on either the race of victims or the race of defendants. The Court discounted the disparities shown by the Bal-dus study on the ground that the research (1) showed substantial flaws in the data base, as shown in tests revealing coding errors and mismatches between items on the Procedural Reform Study (PRS) and Comprehensive Sentencing Study (CSS) questionnaires; (2) lacked accuracy and showed flaws in the models, primarily because the models do not measure decisions based on knowledge available to decision-maker and only predicts outcomes in 50 percent of the cases; and (3) demonstrated multi-collinearity among model variables, showing interrelationship among the variables and consequently distorting relationships, making interpretation difficult.
The district court further held that even if a prima facie case had been established, the state had successfully rebutted the showing because: (1) the results were not the product of good statistical methodology, (2) other explanations for the study results could be demonstrated, such as, white victims were acting as proxies for aggravated cases and that black-victim cases, and (3) black-victim cases, being left cases, and (3) black-victim cases being left behind at the life sentence and voluntary manslaughter stages, are less aggravated and more mitigated than the white-victim cases disposed of in similar fashion.
The district court concluded that petitioner failed to carry his ultimate burden of persuasion, because there is no consistent statistically significant evidence that the death penalty is being imposed on the basis of the race of defendant. In particular there was no statistically significant evidence produced to show that prosecutors are seeking the death penalty or juries are imposing the death penalty because the defendant is black or the victim is white. Petitioner conceded that the study is incapable of demonstrating that he was singled out for the death penalty because of the race of either himself or his victim, and, therefore, petitioner failed to demonstrate that racial considerations caused him to receive the death penalty.
We adopt the following approach in addressing the argument that the district court erred in refusing to hold that the Georgia statute is unconstitutionally applied in light of the statistical evidence. First, we briefly describe the statistical Baldus study that was done in this case. Second, we discuss the evidentiary value such studies have in establishing the ultimate facts that control a constitutional decision. Third, we discuss the constitutional law in terms of what must be proved in order for petitioner to prevail on an argument that a state capital punishment law is unconstitutionally applied because of race discrimination. Fourth, we discuss whether a generalized statistical study such as this could ever be sufficient to prove the allegations of ultimate fact necessary to sustain a successful constitutional attack on a defendant’s sentence. Fifth, we discuss whether, this study is valid to prove what it purports to prove. Sixth, we decide that this particular study, assuming its validity and that it proves what it claims to prove, is insufficient to either require or support a decision for petitioner.
In summary, we affirm the district court on the ground that, assuming the validity of the research, it would not support a *887decision that the Georgia law was being unconstitutionally applied, much less would it compel such a finding, the level which petitioner would have to reach in order to prevail on this appeal.
The Baldus Study
The Baldus study analyzed the imposition of sentence in homicide cases to determine the level of disparities attributable to race in the rate of the imposition of the death sentence. In the first study, Procedural Reform Study (PRS), the results revealed no race-of-defendant effects whatsoever, and the results were unclear at that stage as to race-of-victim effects.
The second study, the Charging and Sentencing Study (CSS), consisted of a random stratified sample of all persons indicted for murder from 1973 through 1979. The study examined the cases from indictment through sentencing. The purpose of the study was to estimate racial effects that were the product of the combined effects of all decisions from the point of indictment to the point of the final death-sentencing decision, and to include strength of the evidence in the cases.
The study attempted to control for all of the factors which play into a capital crime system, such as aggravating circumstances, mitigating circumstances, strength of evidence, time period of imposition of sentence, geographical areas (urban/rural), and race of defendant and victim. The data collection for these studies was exceedingly complex, involving cumbersome data collection instruments, extensive field work by multiple data collectors and sophisticated computer coding, entry and data cleaning processes.
Baldus and Woodworth completed a multitude of statistical tests on the data consisting of regression analysis, indexing factor analysis, cross tabulation, and triangulation. The results showed a 6% racial effect systemwide for white victim, black defendant cases with an increase to 20% in the mid-range of cases. There was no suggestion that a uniform, institutional bias existed that adversely affected defendants in white victim cases in all circumstances, or a black defendant in all cases.
The object of the Baldus study in Fulton County, where McCleskey was convicted, was to determine whether the sentencing pattern disparities that were observed statewide with respect to race of the victim and race of defendant were pertinent to Fulton County, and whether the evidence concerning Fulton County shed any light on Warren McCleskey’s death sentence as an aberrant death sentence, or whether racial considerations may have played a role in the disposition of his case.
.Because there were only ten cases involving police officer victims in Fulton County, statistical analysis could not be utilized effectively. Baldus conceded that it was difficult to draw any inference concerning the overall race effect in these cases because there had only been one death sentence. He concluded that based on the data there was only a possibility that a racial factor existed in McCleskey’s case.
Social Science Research Evidence
To some extent a broad issue before this Court concerns the role that social science is to have in judicial decisionmaking. Social science is a broad-based field consisting of many specialized discipline areas, such as psychology, anthropology, economics, political science, history and sociology. Cf. Sperlich, Social Science Evidence and the Courts: Reaching Beyond the Advisory Process, 63 Judicature 280, 283 n. 14 (1980). Research consisting of parametric and nonparametric measures is conducted under both laboratory controlled situations and uncontrolled conditions, such as real life observational situations, throughout the disciplines. The broad objectives for social science research are to better understand mankind and its institutions in order to more effectively plan, predict, modify and enhance society’s and the individual’s circumstances. Social science as a nonex-act science is always mindful that its research is dealing with highly complex behavioral patterns and institutions that exist in a highly technical society. At best, this *888research “models” and “reflects” society and provides society with trends and information for broad-based generalizations. The researcher’s intent is to use the conclusions from research to predict, plan, describe, explain, understand or modify. To utilize conclusions from such research to explain the specific intent of a specific behavioral situation goes beyond the legitimate uses for such research. Even when this research is at a high level of exactness, in design and results, social scientists readily admit their steadfast hesitancies to conclude such results can explain specific behavioral actions in a certain situation.
The judiciary is aware of the potential limitations inherent in such research: (1) the imprecise nature of the discipline; (2) the potential inaccuracies in presented data; (3) the potential bias of the researcher; (4) the inherent problems with the methodology; (5) the specialized training needed to assess and utilize the data competently, and (6) the debatability of the appropriateness for courts to use empirical evidence in decisionmaking. Cf Henry, Introduction: A Journey into the Future— The Role of Empirical Evidence in Developing Labor Law, 1981 U.Ill.L.Rev. 1, 4; Sperlich, 63 Judicature at 283 n. 14.
Historically, beginning with “Louis Bran-déis’ use of empirical evidence before the Supreme Court ... persuasive social science evidence has been presented to the courts.” Forst, Rhodes & Wellford, Sentencing and Social Science: Research for the Formulation of Federal Guidelines, 7 Hofstra L.Rev. 355 (1979). See Muller v. Oregon, 208 U.S. 412, 28 S.Ct. 324, 52 L.Ed. 551 (1908); Brown v. Board of Education, 347 U.S. 483, 74 S.Ct. 686, 98 L.Ed. 873 (1954). The Brandéis, brief presented social facts as corroborative in the judicial decisionmaking process. O’Brien, Of Judicial Myths, Motivations and Justifications: A Postscript on Social Science and the Law, 64 Judicature 285, 288 (1981). The Brandéis brief “is a well-known technique for asking the court to take judicial notice of social facts.” Sperlich, 63 Judicature at 280, 285 n. 31. “It does not solve the problem of how to bring valid scientific materials to the attention of the court____ Brandéis did not argue that the data were valid, only that they existed____ The main contribution ... was to make extra-legal data readily available to the court.” Id.
This Court has taken a position that social science research does play a role in judicial decisionmaking in certain situations, even in light of the limitations of such research. Statistics have been used primarily in cases addressing discrimination.
Statistical analysis is useful only to show facts. In evidentiary terms, statistical studies based on correlation are circumstantial evidence. They are not direct evidence. Teamsters v. United States, 431 U.S. 324, 340, 97 S.Ct. 1843, 1856, 52 L.Ed.2d 396 (1977). Statistical studies do not purport to state what the law is in a given situation. The law is applied to the facts as revealed by the research.
In this case the realities examined, based on a certain set of facts reduced to data, were the descriptive characteristics and numbers of persons being sentenced to death in Georgia. Such studies reveal, as circumstantial evidence through their study analyses and results, possible, or probable, relationships that may exist in the realities studied.
The usefulness of statistics obviously depends upon what is attempted to be proved by them. If disparate impact is sought to be proved, statistics are more useful than if the causes of that impact must be proved. Where intent and motivation must be proved, the statistics have even less utility. This Court has said in discrimination cases, however, “that while statistics alone usually cannot establish intentional discrimination, under certain limited circumstances they might.” Spencer v. Zant, 715 F.2d 1562, 1581 (11th Cir.1983), on pet. for reh’g and for reh’g en banc, 729 F.2d 1293 (11th Cir.1984). See also Eastland v. Tennessee Valley Authority, 704 F.2d 613, 618 (11th Cir.1983); Johnson v. Uncle Ben’s, Inc., 628 F.2d 419, 421 (5th Cir.1980), cert. denied, 459 U.S. *889967, 103 S.Ct. 293, 74 L.Ed.2d 277 (1982). These limited circumstances are where the statistical evidence of racially disproportionate impact is so strong as to permit no inference other than that the results are the product of a racially discriminatory intent or purpose. See Smith v. Balkcom, 671 F.2d 858 (5th Cir. Unit B), cert. denied, 459 U.S. 882, 103 S.Ct. 181, 74 L.Ed.2d 148 (1982).
Statistical evidence has been received in two ways. The United States Supreme Court has simply recognized the existence of statistical studies and social science research in making certain decisions, without such studies being subject to the rigors of an evidentiary hearing. Muller v. Oregon, 208 U.S. 412, 28 S.Ct. 324, 52 L.Ed. 551 (1908); Fowler v. North Carolina, 428 U.S. 904, 96 S.Ct. 3212, 49 L.Ed.2d 1212 (1976); Woodson v. North Carolina, 428 U.S. 280, 96 S.Ct. 2978, 49 L.Ed.2d 944 (1976); Jurek v. Texas, 428 U.S. 262, 96 S.Ct. 2950, 49 L.Ed.2d 929 (1976); Proffitt v. Florida, 428 U.S. 242, 96 S.Ct. 2960, 49 L.Ed.2d 913 (1976); Gregg v. Georgia, 428 U.S. 153, 96 S.Ct. 2909, 49 L.Ed.2d 859 (1976). The “Supreme Court, for example, encountered severe criticism and opposition to its rulings on desegregation of public schools, the exclusionary rule, and the retroactivity of its decisions, precisely because the court relied on empirical generalization.” O’Brien, The Seduction of the Judiciary: Social Science and the Courts, 64 Judicature 8,19 (1980). In each of these situations the Court “focused” beyond the specifics of the case before it to the “institutions” represented and through a specific ruling effected changes in the institutions. On the other hand, statistical evidence may be presented in the trial court through direct testimony and cross-examination on statistical information that bears on an issue. Such evidence is examined carefully and subjected to the tests of relevancy, authenticity, probativeness and credibility. Cf. Henry, 1981 U.Ill.L.Rev. at 8.
One difficulty with statistical evidence is that it may raise more questions than it answers. This Court reached that conclusion in Wilkins v. University of Houston, 654 F.2d 388 (5th Cir. Unit A 1981). In Wilkins this Court held that “[mjultiple regression analysis is a relatively sophisticated means of determining the effects that any number of different factors have on a particular variable.” Id. at 402-03. This Court noted that the methodology “is subject to misuse and thus must be employed with great care.” Id. at 403. Procedurally, when multiple regression is used “it will be the subject of expert testimony and knowledgeable cross-examination from both sides. In this manner, the validity of the model and the significance of its results will be fully developed at trial, allowing the trial judge to make an informed decision as to the probative value of the analysis.” Id. Having done this, the Wilkins Court, in an employment discrimination case, held “the statistical evidence associated with the multiple regression analysis is inconclusive, raising more questions than it answers.” Id.
Even if the statistical evidence is strong there is generally a need for additional evidence. In Wade v. Mississippi Cooperative Extension Serv., 528 F.2d 508 (5th Cir.1976), the results drawn from the multivariate regression analysis were supported by additional evidence. Id. at 517. In Wade the statistics did not “stand alone” as the sole proof of discrimination.
Much has been written about the relationship of law and social science. “If social science cannot produce the required answers, and it probably cannot, its use is likely to continue to lead to a disjointed incrementalism.” Daniels, Social Science And Death Penalty Cases, 1 Law & Pol’y Q. 336, 367 (1979). “Social science can probably make its greatest contribution to legal theory by investigating the causal forces behind judicial, legislative and administrative decisionmaking and by probing the general effects of such decisions.” Na-gel, Law And The Social Sciences: What Can Social Science Contribute?, 356 A.B. A.J. 356, 357-58 (1965).
With these observations, this Court accepts social science research for what the *890social scientist should claim for it. As in all circumstantial evidence cases, the inferences to be drawn from the statistics are for the factfinder, but the statistics are accepted to show the circumstances.
Racial Discrimination, the Death Penalty, and the Constitution
McCleskey contends his death sentence is unconstitutional because Georgia’s death penalty is discriminatorily applied on the basis of the race of the defendant and the victim. Several different constitutional bases for this claim have been asserted. McCleskey relies on the arbitrary, capricious and irrational components of the prohibition of cruel and unusual punishment in the Eighth Amendment and the equal protection clause of the Fourteenth Amendment. The district court thought that with respect to race-of-the-victim discrimination the petitioner more properly stated a claim under the due process clause of the Fourteenth Amendment.
Claims of this kind are seldom asserted with a degree of particularity, and they generally assert several constitutional precepts. On analysis, however, there seems to be little difference in the proof that might be required to prevail under any of the three theories.
In Furman v. Georgia, 408 U.S. 238, 92 S.Ct. 2726, 33 L.Ed.2d 346 (1972), the Supreme Court struck down the Georgia death penalty system on Eighth Amendment grounds, with several of the concurring justices holding that the system operated in an arbitrary and capricious manner because there was no rational way to distinguish the few cases in which death was imposed from the many in which it was not. Id. at 313, 92 S.Ct. at 2764 (White, J., concurring); id. at 309-10, 92 S.Ct. at 2762-63 (Stewart, J. concurring). Although race discrimination in the imposition of the death penalty was not the basis of the decision, it was one of several concerns addressed in both the concurring and dissenting opinions. See id. at 249-52, 92 S.Ct. at 2731-33 (Douglas, J. concurring); id. at 309-10, 92 S.Ct. at 2762-63 (Stewart, J. concurring); id. at 364-65, 92 S.Ct. at 2790-91 (Marshall, J., concurring); id. at 389-90 n. 12, 92 S.Ct. at 2803-04 n. 12 (Burger, C.J., dissenting); id. at 449, 92 S.Ct. at 2833 (Powell, J., dissenting).
Four years later, the Supreme Court approved the redrawn Georgia statute pursuant to which McCleskey was tried and sentenced. Gregg v. Georgia, 428 U.S. 153, 96 S.Ct. 2909, 49 L.Ed.2d 859 (1976). At the same time the Court approved statutes from Florida and Texas which, like Georgia, followed a guided discretion approach, but invalidated the mandatory sentencing procedure of North Carolina and Louisiana. Proffitt v. Florida, 428 U.S. 242, 96 S.Ct. 2960, 49 L.Ed.2d 913 (1976); Jurek v. Texas, 428 U.S. 262, 96 S.Ct. 2950, 49 L.Ed.2d 929 (1976); Woodson v. North Carolina, 428 U.S. 280, 96 S.Ct. 2978, 49 L.Ed.2d 944 (1976); Roberts v. Louisiana, 428 U.S. 325, 96 S.Ct. 3001, 49 L.Ed.2d 974 (1976).
Since Gregg, we have consistently held that to state a claim of racial discrimination in the application of a constitutional capital statute, intent and motive must be alleged. Sullivan v. Wainwright, 721 F.2d 316, 317 (11th Cir.1983) (statistical impact studies insufficient to show state system “intentionally discriminated against petitioner”), petition for stay of execution denied, 464 U.S. 109, 104 S.Ct. 450, 78 L.Ed.2d 210 (1983); Adams v. Wainwright, 709 F.2d 1443, 1449 (11th Cir.1983) (requiring “a showing of an intent to discriminate” or “evidence of disparate impact ... so strong that the only permissible inference' is one of intentional discrimination”), cert. denied, — U.S. —104 S.Ct. 745, 79 L.Ed.2d 203 (1984); Smith v. Balkcom, 671 F.2d 858, 859 (5th Cir.Unit B) (requiring “circumstantial or statistical evidence of racially disproportionate impact ... so strong that the results permit no other inference but that they are the product of a racially discriminatory intent or purpose”), cert. denied, 459 U.S. 882, 103 S.Ct. 181, 74 L.Ed.2d 148 (1982).
Initially in Spinkellink v. Wainwright, 578 F.2d 582 (5th Cir.1978), cert. denied, 440 U.S. 976, 99 S.Ct. 1548, 59 L.Ed.2d 796 (1979), the Court rejected Eighth and Four*891teenth Amendment claims that the Florida death penalty was being applied in a discriminatory fashion on the basis of the victim’s race. The Spinkellink Court read Gregg and its companion cases “as holding that if a state follows a properly drawn statute in'imposing the death penalty, then the arbitrariness and capriciousness — and therefore the racial discrimination condemned in Furman — have been conclusively removed.” Id. at 613-14. Spinkellink can not be read to foreclose automatically all Eighth Amendment challenges to capital sentencing conducted under a facially constitutional statute. In Godfrey v. Georgia, 446 U.S. 420,100 S.Ct. 1759, 64 L.Ed.2d 398 (1980), the Supreme Court sustained an Eighth Amendment challenge to a Georgia death sentence because the Georgia court’s construction of a portion of that facially valid statute left no principled way to distinguish the cases where the death penalty was imposed from those in which it was not. See Proffitt v. Wainwright, 685 F.2d 1227, 1261 n. 52 (11th Cir.1982). Nevertheless, neither Godfrey nor Proffitt undermines this Court’s prior and subsequent pronouncements in Spinkellink, Smith, Adams, and Sullivan regarding the amount of disparate impact that must be shown under either an Eighth Amendment or equal protection analysis.
As the district court here pointed out, such a standard indicates an analytical nexus between Eighth Amendment claims and a Fourteenth Amendment equal protection claim. McCleskey v. Zant, 580 F.Supp. 338, 347 (N.D.Ga.1984). Where an Eighth Amendment claim centers around generalized showings of disparate racial impact in capital sentencing, such a connection is inescapable. Although conceivably the level or amount of disparate racial impact that would render a state’s capital sentencing system arbitrary and capricious under the Eighth Amendment might differ slightly from the level or amount of disparate racial impact that would compel an inference of discriminatory intent under the equal protection clause of the Fourteenth Amendment, we do not need to decide whether there could be a difference in magnitude that would lead to opposite conclusions on a system’s constitutionality depending on which theory a claimant asserts.
A successful Eighth Amendment challenge would require proof that the race factor was operating in the system in such a pervasive manner that it could fairly be said that the system was irrational, arbitrary and capricious. For the same reasons that the Baldus study would be insufficient to demonstrate discriminatory intent or unconstitutional discrimination in the Fourteenth Amendment context, it would be insufficient to show irrationality, arbitrariness and capriciousness under any kind of Eighth Amendment analysis.
The district court stated that were it writing on a clean slate, it would characterize McCleskey’s claim as a due process claim. The court took the position that McCleskey’s argument, while couched in terms of “arbitrary and capricious,” fundamentally contended that the Georgia death penalty was applied on the basis of a morally impermissible criterion: the race of the victim.
The district court’s theory derives some support from the Supreme Court’s decision in Zant v. Stephens, 462 U.S. 862, 103 S.Ct. 2733, 77 L.Ed.2d 235 (1983). The Court there recognized that a state may not attach the “aggravating” label as an element in capital sentencing to factors that are constitutionally impermissible or totally irrelevant to the sentencing process, such as race. If that were done, the Court said, “due process would require that the jury’s decision to impose death be set aside.” Id. 462 U.S. at —, 103 S.Ct. at 2747, 77 L.Ed.2d at 255. From this language it is clear that due process would prevent a state from explicitly making the murder of a white victim an aggravating circumstance in capital sentencing. But where the statute is facially neutral, a due process claim must-be supported by proof that a state, through its prosecutors, jurors, and judges, has implicitly attached the aggravating label to race.
*892Even if petitioner had characterized his claim as one under the due process clause, it would not have altered the legal standard governing the showing he must make to prevail. The application of the due process clause is “an uncertain enterprise which must discover what ‘fundamental fairness’ consists of in a particular situation by first considering any relevant precedents and then by assessing the several interests that are at stake.” Lassiter v. Department of Social Services, 452 U.S. 18, 24-25, 101 S.Ct. 2153, 2158-2159, 68 L.Ed.2d 640 (1981). Due process also requires the assessment of the risk that the procedures being used will lead to erroneous decisions. Mathews v. Eldridge, 424 U.S. 319, 335, 96 S.Ct. 893, 903, 47 L.Ed.2d 18 (1976). Where a due process claim requires a court to determine whether the race of the victim impermissibly affected the capital sentencing process, decisions under the equal protection clause, characterized as “central to the Fourteenth Amendment’s prohibition of discriminatory action by the State,” Rose v. Mitchell, 443 U.S. 545, 554-55, 99 S.Ct. 2993, 2999-3000, 61 L.Ed.2d 739 (1979), are certainly “relevant precedents” in the assessment of the risk of erroneous decisions. Thus, as in the equal protection context, the claimant under a due process theory must present evidence which establishes that in the capital sentencing process race “is a motivating factor in the decision.” Village of Arlington Heights v. Metropolitan Housing Development Corp., 429 U.S. 252, 266, 97 S.Ct. 555, 563, 50 L.Ed.2d 450 (1977).
Due process and cruel and unusual punishment cases do not normally focus on the intent of the governmental actor. But where racial discrimination is claimed, not on the basis of procedural faults or flaws in the structure of the law, but on the basis of' the decisions made within that process, then purpose, intent and motive are a natural component of the proof that discrimination actually occurred.
The Supreme Court has clearly held that to prove a constitutional claim of racial discrimination in the equal protection context, intent, purpose, and motive are necessary components. Washington v. Davis, 426 U.S. 229, 238-42, 96 S.Ct. 2040, 2046-49, 48 L.Ed.2d 597 (1976). A showing of a disproportionate impact alone is not sufficient to prove discriminatory intent unless no other reasonable inference can be drawn. Arlington Heights, 429 U.S. at 264-66, 97 S.Ct. at 562-64. This Circuit has consistently applied these principles of law. Adams v. Wainwright, 709 F.2d 1443, 1449 (11th Cir.1983), cert. denied, — U.S. —, 104 S.Ct. 745, 79 L.Ed.2d 203 (1984); Sullivan v. Wainwright, 721 F.2d 316, 317 (11th Cir.1983).
We, therefore, hold that 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.
Generalized Statistical Studies and the Constitutional Standard
The question initially arises as to whether any statewide study suggesting a racial disparity in the application of a state’s death penalty could ever support a constitutional attack on a defendant’s sentence. The answer lies in whether the statistical study is sufficient evidence of the ultimate fact which must be shown.
In 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), this Court said:
In some instances, circumstantial or statistical evidence of racially disproportionate impact may be so strong that the results permit no other inference but that they are the product of a racially discriminatory intent or purpose.
This statement has apparently caused some confusion because it is often cited as a proposition for \vhich it does not stand. Petitioner argues that his statistical study *893shows a strong inference that there is a disparity based on race. That is only the first step, however. The second step focuses on how great the disparity is. Once the disparity is proven, the question is whether-that disparity is sufficient to compel a conclusion that it results from discriminatory intent and purpose. The key to the problem lies in the principle that the proof, no matter how strong, of some disparity is alone insufficient.
In Spinkellink v. Wainwright, 578 F.2d 582, 612 (5th Cir.1978), cert. denied, 440 U.S. 976, 99 S.Ct. 1548, 59 L.Ed.2d 796 (1979), the petitioner claimed the Florida statute was being applied in a discriminatory fashion against defendants murdering whites, as opposed to blacks, in violation of the cruel and unusual punishment and equal protection components of the Constitution. Evidence of this disparity was introduced through expert witnesses. The court assumed for sake of argument the accuracy of petitioner’s statistics but rejected the Eighth Amendment argument. The court rejected the equal protection argument because the disparity shown by petitioner’s statistics could not prove racially discriminatory intent or purpose as required by Washington v. Davis, 426 U.S. 229, 96 S.Ct. 2040, 48 L.Ed.2d 597 (1976), and Village of Arlington Heights v. Metropolitan Housing Development Corp., 429 U.S. 252, 97 S.Ct. 555, 50 L.Ed.2d 450 (1977). 578 F.2d at 614-16.
In Adams v. Wainwright, 709 F.2d 1443 (11th Cir.1983), cert. denied, — U.S.—, 104 S.Ct. 745, 79 L.Ed.2d 203 (1984), the court, in denying an evidentiary hearing, accepted statistics which arguably tended to support the claim that the Florida death penalty was imposed disproportionately in cases involving white victims. The court then said:
Disparate impact alone is insufficient to establish a violation of the fourteenth amendment. There must be a showing of an intent to discriminate____ Only if the evidence of disparate impact is so strong that the only permissible inference is one of intentional discrimination will it alone suffice.
709 F.2d at 1449 (citations omitted). Here again, in commenting on the strength of the evidence, the court was referring not to the amount or quality of evidence which showed a disparate impact, but the amount of disparate impact that would be so strong as to lead inevitably to a finding of motivation and intent, absent some other explanation for the disparity.
In commenting on the proffer of the Bal-dus study in another case, Justice Powell wrote in dissent from a stay of execution pending en banc consideration of this case:
If the Baldus study is similar to the several studies filed with us in Sullivan v. Wainwright, 464 U.S. 109, 104 S.Ct. 450,78 L.Ed.2d 210 (1983), the statistics in studies of this kind, many of which date as far back as 1948, are merely general statistical surveys that are hardly particularized with respect to any alleged “intentional” racial discrimination. Surely, no contention can be made that the entire Georgia judicial system, at all levels, operates to discriminate in all cases. Arguments to this effect may have been directed to the type of statutes addressed in Furman v. Georgia, 408 U.S. 238 [92 S.Ct. 2726, 33 L.Ed.2d 346] (1972). As our subsequent cases make clear, such arguments cannot be taken seriously under statutes approved in Gregg.
Stephens v. Kemp, 464 U.S. 1027,1030, n. 2, 104 S.Ct. 562, 564 n. 2, 78 L.Ed.2d 370, 374 n. 2 (1984) (Powell, J., dissenting).
The lesson from these and other cases must be that generalized statistical studies are of little use in deciding whether a particular defendant has been unconstitutionally sentenced to death. As to whether the system can survive constitutional attack, statistical studies at most are probative of how much disparity is present, but it is a legal question as to how much disparity is required before a federal court will accept it as evidence of the constitutional flaws in the system.
This point becomes especially critical to a court faced with a request for an evidentia-ry hearing to produce future studies which *894will undoubtedly be made. 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 evi-dentiary hearing as to studies which do nothing more than show an unexplainable disparity. Generalized studies would appear to have little hope of excluding every 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 at 859.
This is not to recede from the general proposition that statistical studies may reflect a disparity so great as to inevitably lead to a conclusion that the disparity results from intent or motivation. As decided by this opinion, the Baldus studies demonstrate that the Georgia system does not contain the level of disparity required to meet that constitutional standard.
Validity of the Baldus Study
The social science research of Professor Baldus purports to reveal, through statistical analysis, disparities in the sentencing of black defendants in white victim cases in Georgia. A study is valid if it measures what it purports to measure. Different studies have different levels of validity. The level of the validity of the study is directly related to the degree to which the social scientist can rely on the findings of the study as measuring what it claims to measure.
The district court held the study to be invalid because of perceived errors in the data base, the deficiencies in the models, and the multi-collinearity existing between the independent variables. We hold in this case that even if the statistical results are accepted as valid, the evidence fails to challenge successfully the constitutionality of the Georgia system. Because of this decision, it is not necessary for us to determine whether the district court was right or wrong in its faulting of the Baldus study.
The district court undertook an extensive review of the research presented. It received, analyzed and dealt with the complex statistics. The district court is to be commended for its outstanding endeavor in the handling of the detailed aspects of this case, particularly in light of the consistent arguments being made in several cases based on the Baldus study. Any decision that the results of the Baldus study justify habeas corpus relief would have to deal with the district court’s findings as to the study itself. Inasmuch as social science research has been used by appellate courts in decisionmaking, Muller v. Oregon, 208 U.S. 412, 419-21, 28 S.Ct. 324, 325-26, 52 L.Ed. 551 (1908), and has been tested like other kinds of evidence at trial, see Spink-ellink v. Wainwright, 578 F.2d 582, 612-13 (5th Cir.1978), there is a question as to the standard of review of a trial court’s finding based on a highly complex statistical study.
Findings of fact are reviewed under the clearly erroneous standard which the Supreme Court has defined as: “[a] finding is ‘clearly erroneous’ when although there is evidence to support it, the reviewing court on the entire evidence is left with the definite and firm conviction that a mistake has been committed.” United States v. United States Gypsum Co., 333 U.S. 364, 395, 68 S.Ct. 525, 542, 92 L.Ed. 746 (1948).
Whether a disparate impact reflects an intent to discriminate is an ultimate fact which must be reviewed under the clearly erroneous standard. Pullman-Standard v. Swint, 456 U.S. 273, 102 S.Ct. 1781, 72 L.Ed.2d 66 (1982). In Pullman, the Supreme Court said that Fed.R.Civ.P. 52(a)
*895does not make exceptions or purport to exclude certain categories of factual findings from the obligation of a court of appeals to accept a district court’s findings unless clearly erroneous. It does not divide facts into categories; in particular, it does not divide findings of fact into those that deal with ‘ultimate’ and those that deal with ‘subsidiary’ facts.
456 U.S. at 287, 102 S.Ct. at 1789.
There would seem to be two levels of findings based on statistical evidence that must be reviewed: first, the finding concerning the validity of the study itself, and second, the finding of ultimate fact based upon the circumstantial evidence revealed by the study, if valid.
The district court here found the study invalid. The court found the statistics of the study to be particularly troublesome in the areas of the data base, the models and the relationship between the independent variables. McCleskey v. Zant, 580 F.Supp. 338, 379 (N.D.Ga.1984). We pretermit a review of this finding concerning the validity of the study itself. The district court went on to hold that even if the statistics did validly reflect the Georgia system, the ultimate fact of intent to discriminate was not proven. We review this finding of fact by assuming the validity of the study and rest our holding on the decision that the study, even if valid, not only supports the district judge’s decision under the clearly erroneous standard of review, but compels it.
Sufficiency of Baldus Study
McCleskey argues that, although the post-Furman statute in Georgia now yields more predictable results, the race of the victim is a significant, but of course impermissible, factor which accounts for the imposition of the death penalty in many cases. He supports this argument with the sophisticated Baldus statistical study that, after controlling for the legitimate factors that might rationally explain the imposition of the penalty, purportedly reveals significant race-of-the-victim influence in the system; i.e., all other things being equal, white victim crimes are more likely to result in the penalty. Because the Constitution prohibits the consideration of racial factors as justification for the penalty, McCleskey asserts that the discernible racial influence on sentencing renders the operation of the Georgia system infirm.
In addition, McCleskey asserts that the race-of-the-victim influence on the system is particularly significant in the range of cases involving intermediate levels of aggravation (mid-range aggravation cases). He argues that because his case fell within that range, he has established that impermissible racial considerations operated in his case.
We assume without deciding that the Baldus study is sufficient to show what it purports to reveal as to the application of the Georgia death penalty. Baldus concluded that his study showed that systematic and substantial disparities existed in the penalties imposed upon homicide defendants in Georgia based on race of the homicide victim, that the disparities existed at a less substantial rate in death sentencing based on race of defendants, and that the factors of race of the victim and defendant were at work in Fulton County.
A general comment about the limitations on what the Baldus study purports to show, although covered in the subsequent discussion, may be helpful. The Baldus study statistical evidence does not purport to show that McCleskey was sentenced to death because of either his race or the race of his victim. It only shows that in a group involving blacks and whites, all of whose cases are virtually the same, there would be more blacks receiving the death penalty than whites and more murderers of whites receiving the death penalty than murderers of blacks. The statisticians’ “best guess” is that race was a factor in those cases and has a role in sentencing structure in Georgia. These general statements about the results are insufficient to make a legal determination. An analysis must be made as to how much disparity is actually shown by the research.
Accepting the Baldus figures, but not the general conclusion, as accurately reflecting *896the Georgia experience, the statistics are inadequate to entitle McCleskey to relief on his constitutional claim.
The Georgia-based retrospective study consisted of a stratified random sample of 1,066 cases of individuals indicted for murder-death, murder-life and voluntary manslaughter who were arrested between March 28, 1973 and December 31, 1978. The data were compiled from a 41-page questionnaire and consisted of more than 500,000 entries. Through complex statistical analysis, Baldus examined relationships between the dependent variable, death-sentencing rate, and independent variables, nine aggravating and 75 mitigating factors, while controlling for background factors. In 10% of the cases a penalty trial was held, and in 5% of the cases defendants were sentenced to death.
The study subjects the Georgia data to a multitude of statistical analyses, and under each method there is a statistically significant race-of-the-victim effect operating statewide. It is more difficult, however, to ascertain the magnitude of the effect demonstrated by the Baldus study. The simple, unadjusted figures show that death sentences were imposed in 11% of the white victim cases potentially eligible for the death penalty, and in 1% of the eligible black victim cases. After controlling for various legitimate factors that could explain the differential, Baldus still concluded that there was a significant race-of-the-victim effect. The result of Baldus’ most conclusive model, on which McCleskey primarily relies, showed an effect of .06, signifying that on average a white victim crime is 6% more likely to result in the sentence than a comparable black victim crime. Bal-dus also provided tables that showed the race-of-the-victim effect to be most significant in cases involving intermediate levels of aggravation. In these cases, on average, white victim crimes were shown to be 20% more likely to result in the death penalty than equally aggravated black victim crimes.
None of the figures mentioned above is a definitive quantification of the influence of the victim’s race on the overall likelihood of the death penalty in a given case. Nevertheless, the figures all serve to enlighten us somewhat on how the system operates. The 6% average figure is a composite of all cases and contains both low aggravation cases, where the penalty is almost never imposed regardless of the victim’s race, and high aggravation cases, where both white and black victim crimes are likely to result in the penalty. When this figure is related to tables that classify eases according to the level of aggravation, the 6% average figure is properly seen as an aggregate containing both cases in which race of the victim is a discernible factor and those in which it is not.
McCleskey’s evidence, and the evidence presented by the state, also showed that the race-of-the-victim factor diminishes as more variables are added to the model. For example, the bottom line figure was 17% in the very simple models, dropped to 6% in the 230-variable model, and finally fell to 4% when the final 20 variables were added and the effect of Georgia Supreme Court review was considered.
The statistics are also enlightening on the overall operation of the legitimate factors supporting the death sentence. The Baldus study revealed an essentially rational system, in which high aggravation cases were more likely to result in the death sentence than low aggravation cases. As one would expect in a rational system, factors such as torture and multiple victims greatly increased the likelihood of receiving the penalty.
There are important dimensions that the statistics cannot reveal. Baldus testified that the Georgia death penalty system is an extremely complicated process in which no single factor or group of factors determines the outcome of a given case. No single petitioner could, on the basis of these statistics alone, establish that he received the death sentence because, and only because, his victim was white. Even in the mid-range of cases, where the race-of-the-victim influence is said to be strong, legitimate factors justifying the penalty *897are, by the very definition of the mid-range, present in each case.
The statistics show there is a race-of-the-victim relationship with the imposition of the death sentence discernible in enough cases to be statistically significant in the system as a whole. The magnitude cannot be called determinative in any given case.
The evidence in the Baldus study seems to support the Georgia death penalty system as one operating in a rational manner. Although no single factor, or combination of factors, will irrefutably lead to the death sentence in every case, the system in operation follows the pattern the legislature intended, which the Supreme Court found constitutional in Gregg, and sorts out cases according to levels of aggravation, as gauged by legitimate factors. The fundamental Eighth Amendment concern of Fur-man, as discussed in Gregg, which states that “there is no meaningful basis for distinguishing the few cases in which [the death sentence] is imposed from the many in which it is not” does not accurately describe the operation of the Georgia statute. 428 U.S. at 188, 96 S.Ct. at 2932.
Taking the 6% bottom line revealed in the Baldus figures as true, this figure is not sufficient to overcome the presumption that the statute is operating in a constitutional manner. In any discretionary system, some imprecision must be tolerated, and 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.
This conclusion is supported, and possibly even compelled, by recent Supreme Court opinions in Sullivan v. Wainwright, 464 U.S. 109, 104 S.Ct. 450, 78 L.Ed.2d 210 (1983) (denying stay of execution to allow evidentiary hearing on Eighth Amendment claim supported by statistics); Wainwright v. Adams, — U.S.—, 104 S.Ct. 2183, 80 L.Ed.2d 809 (1984) (vacating stay); and Wainwright v. Ford, — U.S. —, 104 S.Ct. 3498, 82 L.Ed.2d 911 (1984) (denying state’s application to vacate stay on other grounds). A plurality of the Court in Ford definitively stated that it had held “in two prior cases that the statistical evidence relied upon by Ford to support his claim of discrimination was not sufficient to raise a substantial ground upon which relief might be granted.” Id. at —, 104 S.Ct. at 3499, 82 L.Ed.2d at 912 (citing Sullivan and Adams). The petitioners in Sullivan, Adams, and Ford all relied on the study by Gross and Mauro of the Florida death penalty system. The bottom line figure in the Gross and Mauro study indicated a race-of-the-victim effect, quantified by a “death odds multiplier,” of about 4.8 to 1. Using a similar methodology, Baldus obtained a death odds multiplier of 4.3 to 1 in Georgia.
It is of course possible that the Supreme Court was rejecting the methodology of the Florida study, rather than its bottom line. It is true that the methodology of the Bal-dus study is superior. The posture of the Florida cases, however, persuades this Court that the Supreme Court was not relying on inadequacies in the methodology of the Florida study. The issue in Sullivan, Adams, and Ford was whether the petitioner’s proffer had raised a substantial ground sufficient to warrant an evidentiary hearing. In that context, it is reasonable to suppose that the Supreme Court looked at the bottom line indication of racial effect and held that it simply was insufficient to state a claim. A contrary assumption, that the Supreme Court analyzed the extremely complicated Gross and Mauro study and rejected it on methodological grounds, is much less reasonable.
Thus, assuming that the Supreme Court in Sullivan, Adams and Ford found the bottom line in the Gross and Mauro study insufficient to raise a constitutional claim, we would be compelled to reach the same result in analyzing the sufficiency of the comparable bottom line in the Baldus study on which McCleskey relies.
McCleskey’s argument about the heightened influence of the race-of-the-victim factor in the mid-range of cases requires a somewhat different analysis. McCleskey’s case falls within the range of cases involv*898ing intermediate levels of aggravation. The Baldus statistical study tended to show that the race-of-the-victim relationship to sentencing outcome was greater in these cases than in cases involving very low or very high levels of aggravation.
The race-of-the-victim effect increases the likelihood of the death penalty by approximately 20% in the mid-range of cases. Some analysis of this 20% figure is appropriate.
The 20% figure in this case is not analogous to a figure reflecting the percentage disparity in a jury composition case. Such a figure represents the actual disparity between the number of minority persons on the jury venire and the number of such persons in the population. In contrast, the 20% disparity in this case does not purport to be an actual disparity. Rather, the figure reflects that the variables included in the study do not adequately explain the 20% disparity and that the statisticians can explain it only by assuming the racial effect. More importantly, Baldus did not testify that he found statistical significance in the 20% disparity figure for mid-range cases, and he did not adequately explain the rationale of his definition of the mid-range of cases. His testimony leaves this Court unpersuaded that there is a rationally classified, well-defined class of cases in which it can be demonstrated that a race-of-the-victim effect is operating with a magnitude approximating 20%.
v Assuming arguendo, however, that the 20% disparity is an accurate figure, it is apparent that such a disparity only in the mid-range cases, and not in the system as a whole, cannot provide the basis for a systemwide challenge. As previously discussed, the system as a whole is operating in a rational manner, and not in a manner that can fairly be labeled arbitrary or capricious. A valid system challenge cannot be made only against the mid-range of cases. Baldus did not purport to define the mid-range of cases; nor is such a definition possible. It is simply not satisfactory to say that the racial effect operates in “close cases” and therefore that the death penalty will be set aside in “close cases.”
As discussed previously, the statistics cannot show that the race-of-the-victim factor operated in a given case, even in the mid-range. Rather, the statistics show that, on average, the race-of-the-victim factor was more likely to affect the outcome in mid-range cases than in those cases at the high and low ends of the spectrum of aggravation. The statistics alone are insufficient to show. that McCleskey’s sentence was determined by the race of his victim, or even that the race of his victim contributed to the imposition of the penalty in his case.
McCleskey’s petition does not surmount the threshold burden of stating a claim on this issue. Aside from the statistics, he presents literally no evidence that might tend to support a conclusion that the race of McCleskey’s victim in any way motivated the jury to impose the death sentence in his case.
Conclusion
The Supreme Court has held that to be constitutional the sentencer in death sentence cases must have some measure of discretion. Gregg v. Georgia, 428 U.S. 153, 96 S.Ct. 2909, 49 L.Ed.2d 859 (1976); Prof-fitt v. Florida, 428 U.S. 242, 96 S.Ct. 2960, 49 L.Ed.2d 913 (1976). The mandatory death sentence statutes were declared unconstitutional. Woodson v. North Carolina, 428 U.S. 280, 96 S.Ct. 2978, 49 L.Ed.2d 944 (1976); Roberts v. Louisiana, 428 U.S. 325, 96 S.Ct. 3001, 49 L.Ed.2d 974 (1976).
The very exercise of discretion means that persons exercising discretion may reach different results from exact duplicates. Assuming each result is within the range of discretion, all are correct in the eyes of the law. It would not make sense for the system to require the exercise of discretion in order to be facially constitutional, and at the same time hold a system unconstitutional in application where that discretion achieved different results for what appear to be exact duplicates, absent the state showing the reasons for the difference. The discretion is narrow, focused *899and directed, but still there is a measure of discretion.
The Baldus approach, however, would take the cases with different results on what are contended to be duplicate facts, where the differences could not be otherwise explained, and conclude that the different result was based on race alone. From a legal perspective, petitioner would argue that since the difference is not explained by facts which the social scientist thinks satisfactory to explain the differences, there is a prima facie case that the difference was based on unconstitutional factors, and the burden would shift to the state to prove the difference in results from constitutional considerations. This approach ignores the realities. It not only ignores quantitative differences in cases: looks, age, personality, education, profession, job, clothes, demeanor, and remorse, just to name a few, but it is incapable of measuring qualitative differences of such things as aggravating and mitigating factors. There are, in fact, no exact duplicates in capital crimes and capital defendants. The type of research submitted here tends to show which of the directed factors were effective, but is of restricted use in showing what undirected factors control the exercise of constitutionally required discretion.
It was recognized when Gregg was decided that the capital justice system would not be perfect, but that it need not be perfect in order to be constitutional. Justice White said:
Petitioner has argued, in effect, that no matter how effective the death penalty may be as a punishment, government, created and run as it must be by humans, is inevitably incompetent to administer it. This cannot be accepted as a proposition of constitutional law. Imposition of the death penalty is surely an awesome responsibility for any system of justice and those who participate in it. Mistakes will be made and discriminations will occur which will be difficult to explain. However, one of society’s most basic tasks is that of protecting the lives of its citizens and one of the most basic ways in which it achieves the task is through criminal laws against murder.
Gregg v. Georgia, 428 U.S. 153, 226, 96 S.Ct. 2909, 2949, 49 L.Ed.2d 859 (1976) (White, J., concurring).
The plurality opinion of the Gregg Court noted:
The petitioner’s argument is nothing more than a veiled contention that Fur-man indirectly outlawed capital punishment by placing totally unrealistic conditions on its use. In order to repair the alleged defects pointed to by the petitioner, it would be necessary to require that prosecuting authorities charge a capital offense whenever arguably there had been a capital murder and that they refuse to plea bargain with the defendant. If a jury refused to convict even though the evidence supported the charge, its verdict would have to be reversed and a verdict of guilty entered or a new trial ordered, since the discretionary act of jury nullification would not be permitted. Finally, acts of executive clemency would have to be prohibited. Such a system, of course, would be totally alien to our notions of criminal justice.
Id. at 199 n. 50, 96 S.Ct. at 2937 n. 50 (opinion of Stewart, Powell, and Stevens, JJ.).
Viewed broadly, it would seem that the statistical evidence presented here, assuming its validity, confirms rather than condemns the system. In a state where past discrimination is well documented, the study showed no discrimination as to the race of the defendant. The marginal disparity based on the race of the victim tends to support the state’s contention that the system is working far differently from the one which Furman condemned. In pre-Furman days, there was no rhyme or reason as to who got the death penalty and who did not. But now, in the vast majority of cases, the reasons for a difference are well documented. That they are not so clear in a small percentage of the cases is no reason to declare the entire^system unconstitutional.
*900The district court properly rejected this aspect of McCleskey’s claim.
INEFFECTIVE ASSISTANCE OF COUNSEL
McCleskey contends his trial counsel rendered ineffective assistance at both guilt/innocence and penalty phases of his trial in violation of the Sixth Amendment.
Although a defendant is constitutionally entitled to reasonably effective assistance from his attorney, we hold that McCleskey has not shown he was prejudiced by the claimed defaults in his counsel’s performance. Ineffective assistance warrants reversal of a conviction only when there is a reasonable probability that the attorney’s errors altered the outcome of the proceeding. A court may decide an ineffectiveness claim on the ground of lack of prejudice without considering the reasonableness of the attorney’s performance. Strickland v. Washington, — U.S.—, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984).
As to the guilt phase of his trial, McCles-key claims that his attorney failed to: (1) interview the prisoner who testified that McCleskey gave a jail house confession; (2) interview and subpoena as defense witnesses the victims of the Dixie Furniture Store robbery; and (3) interview the State’s ballistics expert.
McCleskey demonstrates no prejudice caused by his counsel’s failure to interview Offie Evans. We have held there was no reasonable likelihood that the disclosure of the detective’s statement to Offie Evans would have affected the verdict. There is then no “reasonable probability” that the attorney’s failure to discover this evidence affected the verdict.
As to the robbery victims, McCleskey does not contend that an in-person interview would have revealed something their statements did not. He had an opportunity to cross-examine several of the robbery victims and investigating officers at McCleskey’s preliminary hearing. The reasonableness of the attorney’s investigation need not be examined because there was obviously no prejudice.
The question is whether it was unreasonable not to subpoena the robbery victims as defense witnesses. McCleskey’s attorney relied primarily on an alibi defense at trial. To establish this defense, the attorney put McCleskey on the stand. He also called several witnesses in an attempt to discredit a Dixie Furniture Store employee’s identification of McCleskey and to show that McCleskey’s confession was involuntary. It would have undermined his defense if the attorney had called witnesses to testify as to which robber did the shooting. No prejudice can be shown by failing to subpoena witnesses as a reasonable strategy decision.
McCleskey’s attorney could have reasonably prepared to cross-examine the State’s ballistics expert by reading the expert’s report. No in-person interview was necessary. See Washington v. Watkins, 655 F.2d 1346, 1358 (5th Cir.1981), cert. denied, 456 U.S. 949, 102 S.Ct. 2021, 72 L.Ed.2d 474 (1982). The report was in the prosecutor’s file which the attorney reviewed and no contention has been made that he did not read it.
As to the sentencing phase of his trial, McCleskey asserts his attorney failed to investigate and find character witnesses and did not object to the State’s introduction of prior convictions which had been set aside.
No character witnesses testified for McCleskey at his trial. At the State habeas corpus hearing McCleskey’s attorney testified he talked with both McCleskey and his sister about potential character witnesses. They suggested no possibilities. The sister refused to testify and advised the attorney that their mother was too sick to travel to the site of the trial. McCleskey and his sister took the stand at the State habeas corpus hearing and told conflicting stories. It is clear from the state court’s opinion that it believed the attorney:
Despite the conflicting evidence on his point, ... the Court is authorized in its *901role as fact finder to conclude that Counsel made all inquiries necessary to present an adequate defense during the sentencing phase. Indeed, Counsel could not present evidence that did not exist.
Although this “finding of fact” is stated in terms of the ultimate legal conclusion, implicit in that conclusion is the historical finding that the attorney’s testimony was credible. See Paxton v. Jarvis, 735 F.2d 1306, 1308 (11th Cir.1984); Cox v. Montgomery, 718 F.2d 1036 (11th Cir.1983). This finding of fact is entitled to a presumption of correctness. Based on the facts as testified to by the attorney, he conducted a reasonable investigation for character witnesses.
As evidence of an aggravating circumstance the prosecutor introduced three convictions resulting in life sentences, all of which had been set aside on Fourth Amendment grounds. This evidence could not result in any undue prejudice, because although the convictions were overturned, the charges were not dropped and McCleskey pleaded guilty and received sentences of 18 years. The reduction in sentence was disclosed at trial.
The district court properly denied relief on the ineffectiveness of counsel claim.
DEATH-ORIENTED JURY
Petitioner claims the district court improperly upheld the exclusion of jurors who were adamantly opposed to capital punishment. According to petitioner, this exclusion violated his right to be tried by an impartial and unbiased jury drawn from a representative cross-section of his community. In support of this proposition, petitioner cites two district court opinions from outside circuits. Grigsby v. Mabry, 569 F.Supp. 1273 (E.D.Ark.1983), hearing en banc ordered, No. 83-2113 E.A. (8th Cir. Nov. 8, 1983), argued (March 15, 1984) and Keeten v. Garrison, 578 F.Supp. 1164 (W.D.N.C.1984), rev’d, 742 F.2d 129 (4th Cir.1984). Whatever the merits of those opinions, they are not controlling authority for this Court.
Because both jurors indicated they would not under any circumstances consider imposing the death penalty, they were properly excluded under Witherspoon v. Illinois, 391 U.S. 510, 88 S.Ct. 1770, 20 L.Ed.2d 776 (1968) . See also Boulden v. Holman, 394 U.S. 478, 89 S.Ct. 1138, 22 L.Ed.2d 433 (1969) . Their exclusion did not violate petitioner’s Sixth Amendment rights to an impartial, community-representative jury. Smith v. Balkcom, 660 F.2d 573, 582-83 (5th Cir. Unit B 1981), cert. denied, 459 U.S. 882, 103 S.Ct. 181, 74 L.Ed.2d 148 (1982); Spinkellink v. Wainwright, 578 F.2d 582, 593-94 (5th Cir.1978), cert. denied, 440 U.S. 976, 99 S.Ct. 1548, 59 L.Ed.2d 796 (1979).
THE SANDSTROM ISSUE
The district court rejected McCleskey’s claim that the trial court’s instructions to the jury on the issue of'intent deprived him of due process by shifting from the prosecution to the defense the burden of proving beyond a reasonable doubt each essential element of the crimes for which he was tried. Such burden-shifting is unconstitutional under Sandstrom v. Montana, 442 U.S. 510, 99 S.Ct. 2450, 61 L.Ed.2d 39 (1979).
McCleskey objects to the following portion of the trial court’s instruction to the jury:
One section of our law says that the acts of a person of sound mind and discretion are presumed to be the product of the person’s will, and a person of sound mind and discretion is presumed to intend the natural and probable consequences of his acts, but both of these presumptions may be rebutted.
In its analysis of whether this instruction was unconstitutional under Sandstrom, the district court examined two recent panel opinions of this Circuit, Franklin v. Francis, 720 F.2d 1206 (11th Cir.1983), cert. granted, — U.S.—, 104 S.Ct. 2677, 81 L.Ed.2d 873 (1984), and Tucker v. Francis, 723 F.2d 1504 (11th Cir.), on pet. for reh’g and reh’g en banc, 723 F.2d 1518 (11th Cir.1984). Even though the jury in*902structions in the two cases were identical, Franklin held that the language created a mandatory rebuttable persumption viola-tive of Sandstrom while Tucker held that it created no more than a permissive inference and did not violate Sandstrom. Noting that the challenged portion of the instruction used at McCleskey’s trial was “virtually identical” to the corresponding portions of the charges in Franklin and Tucker, the district court elected to follow Tucker as this Court’s most recent pronouncement on the issue, and it held that Sandstrom was not violated by the charge on intent.
Since the district court’s decision, the en banc court has heard argument in several cases in an effort to resolve the constitutionality of potentially burden-shifting instructions identical to the one at issue here. Davis v. Zant, 721 F.2d 1478 (11th Cir.1983), on pet. for reh’g and reh’g en banc, 728 F.2d 492 (11th Cir.1984); Drake v. Francis, 727 F.2d 990 (11th Cir.), on pet. for reh’g and for reh’g en banc, 727 F.2d 1003 (11th Cir.1984); Tucker v. Francis, 723 F.2d 1504 (11th Cir.), on pet. for reh’g and reh’g en banc, 723 F.2d 1518 (11th Cir.1984). The United States Supreme Court has heard oral argument in Franklin v. Francis, 53 U.S.L.W. 3373 (U.S. Nov. 20, 1984) [No. 83-1590]. However these cases are decided, for the purpose of this decision, we assume here that the intent instruction in this case violated Sandstrom and proceed to the issue of whether that error was harmless.
The Supreme Court requires that “before a federal constitutional error can be harmless, the court must be able to declare a belief that it was harmless beyond a reasonable doubt.” Chapman v. California, 386 U.S. 18, 24, 87 S.Ct. 824, 828, 17 L.Ed.2d 705 (1967). More recently, the Supreme Court has divided over the issue of whether the doctrine of harmless error is ever applicable to burden-shifting presumptions violative of Sandstrom. Reasoning that “[a]n erroneous presumption on a disputed element of the crime renders irrelevant the evidence on the issue because the jury may have relied upon the presumption rather than upon that evidence,” a four-justice plurality held that one of the two tests for harmless error employed by this Circuit — whether the evidence of guilt is so overwhelming that the erroneous instruction could not have contributed to the jury’s verdict — is inappropriate. Connecticut v. Johnson, 460 U.S. 73, 85-87, 103 S.Ct. 969, 976-978, 74 L.Ed.2d 823 (1983). The fifth vote to affirm was added by Justice Stevens, who concurred on jurisdictional grounds. Id. at 88, 103 S.Ct. at 978 (Stevens, J., concurring in the judgment). Four other justices, however, criticized the plurality for adopting an “automatic reversal” rule for Sandstrom error.. Id. at 98, 103 S.Ct. at 983 (Powell, J., dissenting). The Supreme Court has subsequently reviewed another case in which harmless error doctrine was applied to a Sandstrom violation. The Court split evenly once again in affirming without opinion a Sixth Circuit decision holding that “the prejudicial effect of a Sandstrom instruction is largely a function of the defense asserted at trial.” Engle v. Koehler, 707 F.2d 241, 246 (6th Cir.1983), aff’d by an equally divided court, — U.S.—, 104 S.Ct. 1673, 80 L.Ed.2d 1 (1984) (per curiam). In En-gle, the Sixth Circuit distinguished between Sandstrom violations where the defendant has claimed nonparticipation in the crime and those where the defendant has claimed lack of mens rea, holding that only the latter was so prejudicial as never to constitute harmless error. Id. Until the Supreme Court makes a controlling decision on the harmless error question, we continue to apply the standards propounded in our earlier cases.
Since Sandstrom was decided in 1979, this Circuit has analyzed unconstitutional burden-shifting instructions to determine whether they constituted harmless error. See, e.g., Mason v. Balkcom, 669 F.2d 222, 227 (5th Cir. Unit B 1982). In Lamb v. Jernigan, 683 F.2d 1332 (11th Cir.1982), cert. denied, 460 U.S. 1024, 103 S.Ct. 1276, 75 L.Ed.2d 496 (1983), the Court identified two situations in which an unconstitutional burden-shifting instruction might be harm*903less. First, an erroneous instruction may have been harmless if the evidence of guilt was so overwhelming that the error could not have contributed to the jury’s decision to convict. Lamb, 683 F.2d at 1342; Mason, 669 F.2d at 227. In the case before us, the district court based its finding that the Sandstrom violation was harmless on this ground. This Circuit has decided on several occasions that overwhelming evidence of guilt renders a Sandstrom violation harmless. See Jarrell v. Balkcom, 735 F.2d 1242,1257 (11th Cir.1984); Brooks v. Francis, 716 F.2d 780, 793-94 (11th Cir.1983), on pet. for reh’g and for reh’g en banc, 728 F.2d 1358 (11th Cir.1984); Spencer v. Zant, 715 F.2d 1562, 1578 (11th Cir.1983), on pet. for reh’g and for reh’g en banc, 729 F.2d 1293 (11th Cir.1984).
Second, the erroneous instruction may be harmless where the instruction shifts the burden on an element that is not at issue at trial. Lamb, 683 F.2d at 1342. This Circuit has adopted this rationale to find a Sandstrom violation harmless. See Drake v. Francis, 727 F.2d 990, 999 (11th Cir.), on pet. for reh’g and for reh’g en banc, 727 F.2d 1003 (11th Cir.1984); Collins v. Francis, 728 F.2d 1322, 1330-31 (11th Cir.1984), pet. for reh’g en banc denied, 734 F.2d 1481 (11th Cir.1984). There is some indication that even the plurality in Connecticut v. Johnson would endorse this type of harmless error in limited circumstances:
[A] Sandstrom error may be harmless if the defendant conceded the issue of intent____ In presenting a defense such as alibi, insanity, or self-defense, a defendant may in some cases admit that the act alleged by the prosecution was intentional, thereby sufficiently reducing the likelihood that the jury applied the erroneous instruction as to permit the appellate court to consider the error harmless.
460 U.S. at 87, 103 S.Ct. at 978 (citations omitted).
Our review of the record reveals that the Sandstrom violation in this case is rendered harmless error under this second test. Before discussing whether intent was at issue in McCleskey’s trial, however, we note that intent is an essential element of the crime with which he was charged. Georgia law provides three essential elements to the offense of malice murder: (1) a homicide; (2) malice aforethought; and (3) unlawfulness. Lamb v. Jernigan, 683 F.2d at 1336. The “malice” element means the intent to kill in the absence of provocation. Id. The erroneous instruction on intent, therefore, involved an essential element of the criminal offense charged, and the state was required to prove the existence of that element beyond a reasonable doubt. In re Winship, 397 U’S. 358, 364, 90 S.Ct. 1068, 1072, 25 L.Ed.2d 368 (1970). The question therefore becomes whether McCleskey conceded the element of intent by presenting a defense that admits that the act alleged was intentional.
Of course, a defendant in a criminal trial may rely entirely on the presumption of innocence and the State’s burden of proving every element of the crime beyond a reasonable doubt. Connecticut v. Johnson, 460 U.S. at 87 n. 16,103 S.Ct. at 978 n. 16. In such a case, determining whether a defendant had conceded the issue of intent might well be impossible. The record reveals, however, that McCleskey chose not to take that course. Rather, he took the stand at trial and testified that he was not a participant in the Dixie Furniture Store robbery which resulted in the killing of Officer Schlatt. The end of McCleskey’s testimony on direct examination summarizes his alibi defense:
Q. Were you at the Dixie Furniture Store that day?
A. No.
Q. Did you shoot anyone?
A. No, I didn’t.
Q. Is everything you have said the truth?
A. Positive.
In closing argument, McCleskey’s attorney again stressed his client’s alibi defense. He concentrated on undermining the credibility of the eyewitness identifications that *904pinpointed McCleskey as the triggerman and on questioning the motives of the other robbery participants who had testified that McCleskey had fired the fatal shots. McCleskey’s attorney emphasized that
if Mr. McCleskey was in the front of the store and Mr. McCleskey had the silver gun and if the silver gun killed the police officer, then he would be guilty. But that is not the circumstances that have been proven.
Although. McCleskey’s attorney’s arguments were consistent with the alibi testimony offered by McCleskey himself, the jury chose to disbelieve that testimony and rely instead on the testimony of eyewitnesses , and the other participants in the robbery.
We therefore hold that in the course of asserting his alibi defense McCleskey effectively conceded the issue of intent, thereby rendering the .»Sandstrom violation harmless beyond a reasonable doubt. In so holding, we do not imply that whenever a defendant raises a defense of alibi a Sandstrom violation on an intent or malice instruction is automatically rendered harmless error. Nor do we suggest that defendant must specifically argue that intent did not exist in order for the issue of intent to remain before the jury. But where the State has presented overwhelming evidence of an intentional killing and where the defendant raises a defense of nonparticipation in the crime rather than lack cf. mens rea, a Sandstrom violation on an intent instruction such as the one at issue here is harmless beyond a reasonable doubt. See Collins v. Francis, 728 F.2d at 1331; Engle v. Koehler, 707 F.2d at 246.
In this case the officer entered and made it almost to the middle of the store before he was shot twice with a .38 caliber Rossi revolver. The circumstances of this shooting, coupled with McCleskey’s decision to rely on an alibi defense, elevate to mere speculation any scenario that would create a reasonable doubt on the issue of intent. The district court properly denied habeas corpus relief on this issue.
CONCLUSION
The judgment of the district court in granting the petition for writ of habeas corpus is reversed and the petition is hereby denied.
REVERSED and RENDERED.
All of the Judges of the Court concur in the judgment as to the death-oriented jury claim and the ineffective assistance of counsel claim. Judges Tjoflat, Vance and Anderson join in the opinion but each has written separately on the constitutional application of the Georgia death sentence.
Judge Kravitch has written separately to concur only in the harmless error portion of the opinion on the Giglio issue but joins in the opinion on all other issues.
Chief Judge Godbold dissents from the judgment of the Court on the Giglio issue but joins in the opinion on all other issues.
Judges Johnson, Hatchett and Clark dissent from the judgment of the Court on the constitutional application of the Georgia death sentence and the Sandstrom and Giglio issues and each has written a separate dissenting opinion.