Bruce Barksdale, seeking to set aside his seventeen-year-old conviction for aggravated rape, appeals from the district court denial of his petition for a writ of habeas *1117corpus. As the basis for his petition, Barks-dale, who is black, alleges that blacks were systematically excluded from the Orleans Parish grand jury which indicted him and from the petit jury venire which included the jurors who convicted him.1 A panel of this court, with one judge dissenting, agreed with Barksdale’s contentions and reversed the district court. United States ex rel. Barksdale v. Blackburn, 610 F.2d 253 (5th Cir. 1980). The court then voted to rehear this case en banc, United States ex rel. Barksdale v. Blackburn, 616 F.2d 254 (5th Cir. 1980), thus vacating the panel opinion. See Fifth Circuit Local Rule 17. We find that there was no systematic exclusion of blacks from the juries and jury venires in question, and therefore now affirm the judgment of the district court.
I. The Factual Background2
The facts of this case seem to have “been lost in the ‘nice, sharp quillets of the law.’ ”3 On the morning of October 3, 1962, Bruce Barksdale followed a young woman to her apartment building in New Orleans’ French Quarter. He knocked on her door and inquired whether a couch in the hallway was for sale. As the woman opened the door to respond, Barksdale slammed against the door, shoved the woman back into her apartment, and threatened her with a raised hammer. The woman tried to run past Barksdale, but he grabbed her before she could reach the stairway and forcibly brought her back into the apartment. Barksdale then robbed his victim, pushed her into the bedroom, and shoved her face down onto the bed. He placed his knee in the middle of her back, and told her, “I’m not going to hurt you if you do as I tell you.” Barksdale pulled off the woman’s skirt, ordered her to remove her blouse, and tore off her underwear. Then, with the hammer still in his hand, Barksdale raped his victim. He told her, “[y]ou know I am going to have to kill you now.” The woman begged hysterically for her life, and Barksdale relented after requiring her to swear to tell no one of the incident. As he left the apartment, Barksdale grabbed his victim by the throat and gave her a final warning: “If you ever tell anybody about this I will kill you. I have before and I will again, and I better not see you on the streets.”
A short time later, the victim was found in an extremely agitated and distressed condition by her landlord. She was able to give the police a description of her assailant, from which a composite drawing was made. Two workers at a motel across the street from the victim’s apartment also gave the police descriptions of a man with a hammer seen in the vicinity that morning. On the basis of these leads, the police were able to apprehend Barksdale the next morning.
The victim positively identified Barksdale on October 4, the day after the attack, in a lineup at New Orleans police headquarters. The two workmen also identified Barksdale. Clothing seized from Barksdale at the time of his arrest matched the victim’s description of her assailant’s clothes. A hammer similar to the one described by the victim was also found. Scientific tests of Barks-dale’s clothing revealed seminal fluid on the genital region of his garments. Furthermore, cat hair removed from Barksdale’s clothing matched hair taken from the victim’s bed, clothing and pet cat.
*1118On October 5, Barksdale asked to see the arresting officers in order to make a statement. He subsequently dictated a confession that was typed out verbatim by a police lieutenant. The facts in Barksdale’s statement substantially corroborate those related by the rape victim.4
Barksdale was indicted for aggravated rape by an Orleans Parish Grand Jury. Two of the twelve members of that jury were black. Prior to trial, counsel for Barksdale challenged the composition of the general jury venire, the grand jury venire, the petit jury venire and the grand jury itself, alleging systematic exclusion of blacks. The state trial court held a hearing to consider these contentions and developed an extensive record which included the testimony of the Chairman of the Orleans Parish Jury Commission and seven judges of the Orleans Parish Criminal District Court.5 In addition, counsel for Barksdale and the state entered into written stipulations regarding black representation on the venires and the juries for various years. Based on this record, the court denied Barksdale’s challenges.
At trial, Barksdale presented no evidence or testimony in his favor and offered no defense.6 Indeed, except for some limited cross-examination of police officers regarding the voluntariness of the confession, counsel for Barksdale did not cross-examine the victim or other witnesses produced by the state. The accused’s confession, the scientific tests, eyewitness identifications and other evidence all were admitted without objection. The jury found Barksdale guilty as charged and imposed the death penalty. The sentence was later reduced to life imprisonment.
II. Barksdale’s Appeals
Over the past seventeen years, Barksdale has resorted to every available appellate channel, alleging a variety of defects including jury discrimination. The Louisiana Supreme Court heard his first appeal, and, in a lengthy opinion, unanimously found no intentional or systematic exclusion of blacks from the jury system, noting that since Eubanks v. State of Louisiana, 356 U.S. 584, 78 S.Ct. 970, 2 L.Ed.2d 991 (1958), a case which reversed a murder conviction because of grand jury discrimination, “the judges of the parish have adopted a practice of jury selection in keeping with the spirit of the law announced in the Eubanks case.” State v. Barksdale, 247 La. 198, 170 So.2d 374, 380 (1964). Barksdale then presented his jury discrimination claims to the United States Supreme Court, which denied certiorari, 382 U.S. 921, 86 S.Ct. 297, 15 L.Ed.2d 236 (1965). Approximately two years later, the Louisiana Supreme Court denied Barksdale’s habeas petition. State ex rel. Barksdale v. Dees, 252 La. 434, 211 So.2d 318 (1968).7
In 1971, Barksdale filed a petition for a writ of habeas corpus in federal district court. The petition was originally heard by *1119a federal magistrate, and, based on the magistrate’s recommendations, the district court set aside Barksdale’s conviction. The state’s appeal was dismissed. Barksdale v. Henderson, No. 73-1536, cert. denied, 419 U.S. 880, 95 S.Ct. 145, 42 L.Ed.2d 120 (1974). The state then moved to vacate the district court judgment on the ground that the hearing before the magistrate was an improper delegation of authority under Wingo v. Wedding, 418 U.S. 461, 94 S.Ct. 2842, 41 L.Ed.2d 879 (1974). The motion was granted and affirmed on appeal, Barksdale v. Henderson, 519 F.2d 382 (5th Cir.), cert. denied, 422 U.S. 1045, 95 S.Ct. 2662, 45 L.Ed.2d 697 (1975). The case was remanded for an evidentiary hearing, and, after three such hearings,8 the district court finally denied the petition. It found that at “the time of petitioner’s trial the jury commission and the judges were not engaged in invidious racial discrimination and purposeful exclusion of blacks as a class from jury service on the grand and petit juries.”
Barksdale appealed the district court ruling, and a panel of this court, with one judge dissenting, reversed, holding that Barksdale presented an unrebutted prima facie case of racial discrimination. The panel compared the black percentage of the general population of Orleans Parish in 1962 and 1963 with the percentage of blacks appearing on the general jury venire for those years and reasoned that the disparities found proved “the existence of both grand and petit jury discrimination” because “both [the] grand and petit juries were selected from the names which appeared on the general venire.” 610 F.2d at 266. In addition, the panel noted that the sequence of blacks serving on grand juries from 1954 through 1963 in itself “evidences discrimination through limited inclusion.” 610 F.2d at 268. The panel held that the state’s justifications for the disparities were either unsupported or illegal. The state’s contention that different literacy levels for white and black jurors explained the lower level of black participation was held to be “unsupported by the record.” 610 F.2d at 272. The state’s contention that the remainder of the disparity was explained “in terms of the arguably benign system of excusing ‘hardship’ cases” was held to be unacceptable in light of Labat v. Bennett, supra, 365 F.2d 698. Thus, with the state “left without a legitimate non-discriminatory explanation to rebut Barksdale’s prima facie case,” 610 F.2d at 272, the panel set aside the conviction.
III. Is Guilt Irrelevant?9
On this appeal, Barksdale raises only one issue, alleging that the jury system in Orleans Parish systematically excluded blacks from grand jury and petit jury service. Several analytical steps must be taken before this broad issue can be determined, however. Initially it must be determined whether Barksdale proved a prima facie case of jury discrimination. At issue in that determination will be not only how much of a disparity exists between the eligible black population and actual black representation on juries, but also how much of a disparity is needed to prove the ease and what statistical measures of population and jury representation are appropriate. Once a prima facie case has been proved, it must be determined whether the state effectively rebutted that case. Here it will be necessary to examine whether the Orleans Parish system of excusing certain workers on request was a constitutionally permissible means of rebuttal in light of Labat v. Bennett, supra, and related cases.
A preliminary matter is suggested by the fact that Barksdale has never made, and could never make, any colorable claim that he is innocent of the crime for which he was *1120convicted. As Justice Powell stated in his concurring opinion in Schneckloth v. Bustamonte, 412 U.S. 218, 257-58, 93 S.Ct. 2041, 2063, 36 L.Ed.2d 854 (1973), the “central reason” for habeas corpus is “the affording of means, through an extraordinary writ, of redressing an unjust incarceration.” One can legitimately question whether freeing a petitioner who is guilty beyond a reasonable doubt of a heinous crime furthers that central concern.
We are mindful, however, that recently in Rose v. Mitchell, 443 U.S. 545, 99 S.Ct. 2993, 61 L.Ed.2d 739 (1979), Justice Black-mun wrote in Part II of his opinion for the Court that a claim of racial discrimination in the selection of a grand jury foreman presented an issue cognizable on habeas corpus regardless of the guilt or innocence of the petitioner, and regardless of whether the state had previously granted a full and fair hearing on the petitioner’s claim. This was an apparent response to speculation raised by Justice Powell in his dissent in Castaneda where he stated that “claims of grand jury discrimination are not cognizable on federal habeas corpus after Stone v. Powell, 428 U.S. 465, 96 S.Ct. 3037 [49 L.Ed.2d 1067] (1976).” Castaneda v. Partida, 430 U.S. 482, 508 n.1, 97 S.Ct. 1272, 1287 n.1, 51 L.Ed.2d 498 (1977). However, Part II of Justice Blackmun’s opinion was joined by only two justices who joined in the judgment of the Court and by two dissenters (Justices White and Stevens), leading Justice Powell to question its precedential value “for not all of the four Members who join it support even the Court’s judgment.” Rose v. Mitchell, supra, 443 U.S. at 582, n.3, 99 S.Ct. at 3014 n.3 (Powell, J., concurring). Since “the holding of the Court may be viewed as that position taken by those members who concurred in the judgment on the narrowest grounds,” Gregg v. Georgia, 428 U.S. 153, 169 n.15, 96 S.Ct. 2909, 2923 n.15, 49 L.Ed.2d 859 (1976), Justice Powell’s point is well taken. Even if one considers Part II to be a part of the Court’s holding, it may not be dispositive of this case. Justice Blackmun’s opinion primarily addresses the contention of Justice Jackson, dissenting in Cassell v. Texas, 339 U.S. 282, 298, 70 S.Ct. 629, 637, 94 L.Ed. 839 (1950), that discrimination in grand jury selection, absent petit jury discrimination, should never result in reversal of a conviction. Rose v. Mitchell, supra, 443 U.S. at 552, 99 S.Ct. at 2998. It might very well still be an open question whether, in light of the facts and circumstances of a particular case, such grand jury discrimination might be harmless error. If ever there was a case in which harmless error should apply it is this one, in which the grand jury did include two blacks, in which the grand and petit jury selection occurred at a time when great progress was being made in eradicating jury discrimination in Louisiana, in which the evidence was so overwhelming that no grand jury, no matter how selected and constituted, could fail to indict, and in which no serious claim of innocence has ever been raised.
Whatever the precedential value of Part II of Justice Blackmun’s opinion in Rose, it may not be the final word on the subject. As Justice Powell noted in his concurrence:
Whenever a federal court is called upon by a state prisoner to issue a writ of habeas corpus, it is asked to do two things that should be undertaken only with restraint and respect for the way our system of justice is structured. First, as one court of general jurisdiction it is requested to entertain a collateral attack upon the final judgment of another court of general jurisdiction. Second, contrary to principles of federalism, a lower federal court is asked to review not only a state trial court’s judgment, but almost invariably the judgment of the highest court of the State as well. These considerations prompt one to inquire, more critically than this Court ever has, whether it is appropriate to allow the use of habeas corpus by state prisoners who do not seek to protect their personal interest in the justness of their convictions.
Rose v. Mitchell, supra, 443 U.S. at 579-80, 99 S.Ct. at 3012 (footnote omitted). The use of habeas corpus to free guilty prisoners *1121who had a fair and accurate trial is indeed troublesome. In the present case, however, we need not rest on the inappropriateness of habeas corpus since we find that Barks-dale’s claims do not prevail on the merits.10
IY. The Legal Issues
Intentional racial discrimination is the foundation of Barksdale’s claim. “Recent cj.ges have established the fact that an official act is not unconstitutional solely because it has a racially disproportionate impact.” Castaneda v. Partida, supra, 430 U.S. at 493, 97 S.Ct. at 1279, citing Washington v. Davis, 426 U.S. 229, 239, 96 S.Ct. 2040, 2047, 48 L.Ed.2d 597 (1976); Arlington Heights v. Metropolitan Housing Dev. Corp., 429 U.S. 252, 264-65, 97 S.Ct. 555, 563, 50 L.Ed.2d 450 (1977). The evidence presented in this case is statistical; Barks-dale has offered no proof to show that even one qualified black was excluded from jury service. Barksdale is not entitled to relief upon a mere showing of a statistical disparity between black population and black participation in the Orleans Parish jury system, but can prevail only if such a disparity “results from purposeful discrimination.” Castaneda v. Partida, supra, 430 U.S. at 493, 97 S.Ct. at 1279.
Castaneda set out a definitive means of proving discriminatory intent:
Thus, in order to show that an equal protection violation has occurred in the context of grand jury selection, the defendant must show that the procedure employed resulted in substantial under-representation of his case or of the identifiable group to which he belongs. The first step is to establish that the group is one that is a recognizable, distinct class, singled out for different treatment under the laws, as written or as applied.... Next, the degree of underrepresentation must be proved, by comparing the proportion of the group in the total population to the proportion called to serve as grand *1122jurors over a significant period of time.... Finally, as noted above, a selection procedure that is susceptible of abuse or is not racially neutral supports that presumption of discrimination raised by the statistical showing.. .. Once the defendant has shown substantial under-representation of his group, he has made out a prima facie case of discriminatory purpose, and the burden then shifts to the State to rebut that case.
Castaneda v. Partida, supra, 430 U.S. at 494-95, 97 S.Ct. at 1280. There are thus four parts of the jury discrimination test. The plaintiff must first identify a distinct class, then show a significant underrepresentation of that class, and then, finally, support that showing by demonstrating that the selection procedure is susceptible to abuse. The fourth part of the test permits the state to rebut the inference of discriminatory purpose. The test does not eliminate the need to show discriminatory intent, but merely acknowledges that “[i]f a disparity is sufficiently large, then it is unlikely that it is due solely to chance or accident, and, in the absence of evidence to the contrary, one must conclude that racial or other class-related factors entered into the selection process.” Castaneda v. Partida, supra, 430 U.S. at 494 n.13, 97 S.Ct. at 1280 n.13. This procedure does not reveal how large a disparity is required to establish a prima facie case or what statistics should be used in defining that disparity.
The Supreme Court has “never announced mathematical standards for the demonstration of ‘systematic’ exclusion of blacks .... ” Alexander v. Louisiana, 405 U.S. 625, 630, 92 S.Ct. 1221, 1225, 31 L.Ed.2d 536 (1972). Nevertheless, some guidance as to the disparities necessary to raise a prima facie case can be gleaned from Supreme Court precedent. In Swain v. Alabama, 380 U.S. 202, 85 S.Ct. 824, 13 L.Ed.2d 759 (1965), the evidence established that “while Negro males over 21 constitute 26% of all males in the county in this age group, only 10 to 15% of the grand and petit jury panels drawn from the jury box since 1953 have been Negroes [sic], there having been only one case in which the percentage was as high as 23%.” 380 U.S. at 205, 85 S.Ct. at 827-28. The Court concluded that this was insufficient “to make out a prima facie case of invidious discrimination under the Fourteenth Amendment.” 380 U.S. at 206, 85 S.Ct. at 828. While the actual disparities found in Swain range from 11 to 16%, the Court held that purposeful discrimination based on race alone could not be “satisfactorily proved by showing that an identifiable group in a community is underrepresented by as much as 10%.” 380 U.S. at 208-09, 85 S.Ct. at 829. See Gewin, An Analysis of Jury Selection Decisions, appended to Foster v. Sparks, 506 F.2d 805, 828-30 (5th Cir. 1975). This circuit, in Thompson v. Sheppard, 490 F.2d 830 (5th Cir. 1974), cert. denied, 420 U.S. 984, 95 S.Ct. 1415, 43 L.Ed.2d 666 (1974), held that the Jury Commission would not be required to recompose jury lists when there was an 11% disparity between the percentage of blacks in the total population and the percentage of blacks on the jury list.
Whether or not greater disparities constitute prima facie evidence of discrimination depends upon the facts of each case. In Alexander v. Louisiana, supra, 405 U.S. at 630, 92 S.Ct. at 1225, the Court found that the petitioner had established a prima facie case of discrimination because the juror “selection procedures themselves were not racially neutral” and there was a 14% disparity between the presumptively eligible black population and the actual list of prospective jurors. The Court made clear that it did not rely “on statistical improbability alone, for the selection procedures themselves were not racially neutral.” 405 U.S. at 630, 92 S.Ct. at 1225. The 14% disparity was sufficient to create a prima facie case only with other evidence of discrimination. A disparity of 14% was found sufficient to establish a prima facie case in Hernandez v. Texas, 347 U.S. 475, 74 S.Ct. 667, 98 L.Ed. 866 (1954), in light of- the fact that no person with a Mexican or Latin American surname had ever served on a jury commission, grand jury or petit jury in the county. In other cases the Supreme Court has found prima facie cases to be established when *1123there were disparities of 23%, Turner v. Fouche, 396 U.S. 346, 90 S.Ct. 532, 24 L.Ed.2d 567 (1970); 33%, Carter v. Jury Commission, 396 U.S. 320, 90 S.Ct. 518, 24 L.Ed.2d 549 (1970); 25.7%, Jones v. Georgia, 389 U.S. 24, 88 S.Ct. 4, 19 L.Ed.2d 25 (1967); and 33.5%, Whitus v. Georgia, 385 U.S. 545, 87 S.Ct. 643, 17 L.Ed.2d 599 (1967).
While the above cases give some idea of the magnitude of disparity needed to establish a prima facie case, their greatest significance lies in their demonstration that there is no magic figure which proves jury discrimination. Any given disparity means little in isolation; a determination of intentional racial discrimination requires an examination of all of the facts and circumstances of a given case. The Supreme Court cases also do not reveal which statistics should be used to measure the disparities. In particular, at issue is whether general population statistics or more meaningful eligible population statistics should be used where, as here, those statistics are in the record. The inquiry is an important one — a given disparity may increase or decrease substantially depending on which set of statistics is employed.11
Although Castaneda v. Partida, supra, used general population statistics to measure racial disparities, that case should not be read to require using those figures. When Castaneda reached the Supreme Court, it had been tried and appealed to this circuit on the basis of general statistics. It was not until oral argument before the Supreme Court that the State of Texas contended that more narrow eligible population statistics would explain the disparity found by the Court. Castaneda v. Partida, supra, 430 U.S. at 488 n.8, 97 S.Ct. at 1276 n.8. The Court proceeded on the basis of general population statistics because there were “so many implicit assumptions” in the use of the untested eligible population statistics which an appellate court could not make “without a record below in which those assumptions were tested.” Id. In other cases, where the appropriate statistics had been developed in the record, the Court relied on statistics describing the population of blacks presumptively eligible for jury service.12 See, e. g., Alexander v. Louisiana, supra; Swain v. Alabama, supra; Jones v. Georgia, supra; Whitus v. Georgia, supra.
V. The Statistics
The district court and this court have been presented with a multitude of statistics which attempts to describe the Orleans Parish jury system as it existed almost two decades ago. Most of the statistics were proposed by Barksdale’s expert, Dr. Levine, or stipulated to by counsel during either the district court hearing or the state court proceedings. The state, for its part, generally accepted the statistics proposed by Barksdale, although on appeal the state argued in its original brief an even more favorable view of the statistics than that taken by the district court.13 While we do not decline to join the statistical fray, this case proves the danger of uncritical deference to statistics. In the absence of any clear guidelines, persuasive figures can be found to support as well as to undermine the finding of a prima facie case of discrim*1124ination. Depending on the figures compared, the disparity between the actual black participation in the juries and venires and presumptively eligible population may be as small as 4.34%14 or as great as 25.2%.15 But neither of these figures has any meaning unless the facts of this case are examined as a whole. The task of this court is first to determine whether the conglomeration of statistics presented conclusively shows intentional racial discrimination, and then to determine whether the state has effectively rebutted that showing.
Our analysis differs radically from that of the panel majority. First, we find that statistics describing the presumptively eligible black juror population, rather than the general black population, provide the proper starting point for an inquiry into racial disparities in the Parish. Statistics describing the percentage of black males of jury age were provided by Barksdale and the state. Further information regarding the presumptively eligible black population is readily obtainable from the 1960 census figures which Barksdale himself offered in evidence before the federal district court. Second, our analysis places considerably greater emphasis on certain statistics stipulated to by both Barksdale and the state before the state trial court and the district court.
A. The Eligible Population
Barksdale contends that he was indicted by a grand jury and convicted by a petit jury from which blacks were systematically excluded. To assess the merits of this claim, it is necessary to first determine the percentage of the population eligible for grand jury service attributable to blacks, and then to determine the percentage of black jurors and veniremen. According to the statute in effect in 1962, compulsory jury service was limited to males at least 21 years old.16 Jurors had to be literate in English, a resident of the Parish for one year prior to service, and neither under indictment for a crime nor convicted of a felony. In addition, certain persons were occupationally exempt from service.17
*1125Neither the census nor any other source presented to the court contains statistics detailed enough to calculate the exact racial breakdown of the population meeting these statutory criteria. In order to approximate the black percentage of the eligible population, Barksdale’s expert, using a complicated mathematical formula called the Three-Point LeGrangian Interpolation,18 estimated the black male population of Orleans Parish as of 1962 and 1963. He then adjusted that figure to eliminate the estimated proportion of the group which was illiterate or occupationally exempt.
In addition to our reluctance to condemn the state’s jury system on the basis of mere estimates, there are several reasons why we do not accept the approximations of Barksdale’s expert. First of all, the use of 1962 figures ignores the fact that potential jurors had to reside in the Parish for at least one full year before they become eligible for jury service. In addition, the jury wheel is not totally emptied and replaced at any one time, but instead new names are added as the old ones are used. Thus the population .of eligibles on the wheel would normally include some names which had been on it for several months. Furthermore, the city directory, from which the names of jurors were selected, certainly did not add all new residents instantaneously.19 For these reasons, the appropriate date to measure the composition of the jury-eligible population must be well over a year prior to 1962, and we therefore use the more precise figures of the 1960 census rather than 1962 approximations.20
Second, Barksdale’s expert seems to have been overzealous in his adjustment of the eligible population on account of occupational exemptions. His adjustments eliminated all persons categorized as “Salesmen and Sales Clerks” in all but the retail trade. This is certainly a much broader category than the statutory exemption for “commercial travelers.” In the absence of any exact figure for that exemption, we cannot adjust for the “commercial traveler” exemption, and will limit our occupational adjustments to the other categories listed in the statute, specified in the census, and included in the adjustments made by Barks-dale’s expert.21 Finally, while Barksdale’s expert does calculate the proportions of the population with fifth-, sixth- and seventh-grade education as a substitute for the literacy and knowledge requirements for jury service, he emphasizes the fifth-grade figure in making his comparisons. We see no reason to declare erroneous the Louisiana Supreme Court determination that a seventh-grade education approximates the qualifications needed for jury service, State v. Barksdale, supra, 170 So.2d at 382-83, especially in light of the fact that in addition to simple literacy, a juror was required to “understand the duties and obligations of citizenship under a republican form of government.”22 We therefore use a sev*1126enth-grade education figure to approximate the literacy and knowledge requirements for jury service, although we also calculate an estimate of the eligible population with a sixth-grade education. We find the following estimates of the presumptively eligible black population to be the most appropriate:23
Seventh Sixth
Percentage of Blacks in Eligible 28.16%
These statistics will be compared below to the percentage of blacks on the grand jury, the grand jury venire and the petit jury venire.
B. The Racial Composition of the Grand Jury and the Grand Jury Venire
There has been great dispute between the parties over the racial breakdown of the persons who were included in the jury venire. We therefore compare a variety of jury and venire participation figures to the eligible population statistics. At trial, the parties appear to have stipulated that 19.43% of the persons on the jury wheel as of January 1, 1962, were black.24 This figure presumed that all persons of undetermined race were black, a presumption with some support in the record.25 The parties at one point sampled thirteen of a group of undetermineds, and found that seven were black, leading to an alternative presumption that 50% of the undetermineds were black.26 Using that presumption, 16.64% of the persons on the jury wheel as of January 1, 1962, were black. Finally, two out of the twelve persons on the grand jury which indicted Barksdale, as well as the three previous grand juries, were black, yielding a black percentage of 16.67%. These figures for grand jury and venire participation compare to the previously derived figures for eligible population as follows:
SEVENTH-GRADE EDUCATION
Stipulation, Stipulation, Actual Undetermined Undetermined Grand Jury Black* _50% Black** Participation
Percentage of Eligible Blacks in the Eligible Population 26.31% 26.31% 26.31%
Percentage of Blacks on Jury or Jury Venire 19.43% 16.64% 16.67%
Disparity_6.88% 9.67% 9.64%
*1127SIXTH-GRADE EDUCATION
Stipulation, Stipulation, Actual Undetermined Undetermined Grand Jury Black* 50% Black** Participation
Percentage of Eligible Blacks in the Eligible Population 28.16% 28.16% 28.16%
Percentage of Blacks on Jury or Jury Venire 19.43% 16.64% 16.67%
Disparity 8.73% 11.52% 11.49%
In light of the cases discussed, supra, in which the United States Supreme Court held that a prima facie case could not be “satisfactorily proved by showing that an identifiable group in a community is underrepresented by as much as 10 percent,” we find that Barksdale has failed to prove a prima facie case of grand jury discrimination. We acknowledge that the Supreme Court has given no clear guidelines as to what disparity proves a prima facie case. However, in this case the disparities offered to prove a prima facie case of jury discrimination are razor thin; such proof may be easily rebutted.
C. The Statistics for the Petit Jury Venire
While there has been some disagreement between the parties as to which petit jury venire statistics are appropriate, the parties stipulated that the final petit jury venire for 1963, the year of Barksdale’s trial, was 21.86% black.27 This figure presumes that only 32% of the undetermineds were blacks, so it cannot be criticized on the same basis as the grand jury venire stipulation of 19.43% black, which presumed that all undetermineds were black. This final petit jury venire figure compares with the eligible population statistics as follows:
Eligible Eligible Population, Population, Seventh-Grade Sixth-Grade _Education_Education
Percentage of Eligible Blacks in the Eligible Population 26.31% 28.16%
Percentage of Blacks in the Final Petit Jury Venire 21.86% 21.86%
Disparity 4.45% 6.30%
Clearly, these disparities are insufficient to prove a prima facie case.
D. The Sequence of Grand Juries
Apart from the statistical disparities discussed above, Barksdale relies on the sequence of blacks actually serving on Orleans Parish grand juries to prove his discrimination claim.28 Barksdale’s expert testified that the sequence of black grand jurors serving from September 1958 to September 1962 had such a low probability of occurring by chance as to be “non-random.” The state’s expert utilized different statistical tests to arrive at his conclusion that the sequence was consistent with a hypothesis of randomness. The district court came to *1128a conclusion we cannot deem erroneous: “Faced with totally opposing views of competent and qualified experts, this Court finds that the petitioner as to the grand jury has failed to carry his burden of proving invidious racial discrimination based on statistical improbability alone.” Moreover, even if accepted, the contention of Barks-dale’s expert that the grand jurors were not selected randomly proves nothing about racial discrimination. Of course Parish grand jurors were not randomly selected; it is not so contended by the state. The grand jury was selected conscientiously and nonrandomly by the judges of the Orleans Parish Criminal District Court, pursuant to Louisiana statute. The judges testified that they sought to select the best qualified jurors from a venire that, according to Louisiana law, was composed only of citizens possessing specified levels of competence. These same judges testified that, while they did not intentionally exclude blacks from the grand jury, they sought to avoid reducing black representation from the jury venire to the actual grand jury. Presented with a venire in 1962 that was between 16.64 and 19.43% black, it is not surprising that a judge who sought to avoid reduction in black participation would select two black grand jurors on a twelve-man jury. Several of the judges testified that they had to make special efforts to find at least two blacks who were eligible to serve and did not have to be excused because of occupation or hardship. This court should be especially careful not to ascribe invidious motivations to a group of judges who, as noted by the panel majority, were not taking race into account “when they granted excuses in order to reduce the proposed petit venire to the final petit venire.” 610 F.2d at 268. Unfortunately, neither expert squarely addressed the key question: does the sequence of grand juries conclusively prove that the jury selection process intentionally excluded blacks from the grand juries? The answer to that question must be no, because the concept of nonrandomness is every bit as consistent with nonrandom efforts to include blacks as it is with efforts to exclude blacks.
VI. The State’s Rebuttal Evidence
Since we find that Barksdale has not proven a prima facie case of jury discrimination, the state’s rebuttal evidence may seem to be superfluous. But we hold, as an alternative grounds for our decision, that even assuming, arguendo, that Barksdale did meet his initial burden, the state adequately rebutted his case.
There is extensive testimony in the record by judges of the Parish criminal courts and representatives of the Jury Commission regarding the juror selection procedure. Such testimony has considerable importance. Castaneda v. Partida, supra, 430 U.S. at 488 n.8 & 498-99, 97 S.Ct. at 1276-77 n.8 & 1282; Swain v. Alabama, supra, 380 U.S. at 207 n.4 & 209, 85 S.Ct. at 829 n.4 & 830. The judges testified that they did not intentionally include or exclude blacks from the jury venires or the grand or petit juries, but that a disproportionately large number of blacks asked to be excused because of economic hardship. The stipulated testimony of the Jury Commission shows that “an exceedingly large number of the Negro males who appear before the Jury Commissioners disqualify themselves for jury service by stating either that they cannot read or write or that they have had only a very small amount of formal schooling, or by showing that they are self-employed or that their employers will not excuse them from work and will not pay them their wages if they serve on a jury .... ” While simple protestations “of good faith in making individual selections are insufficient to dispel a prima facie case of systematic exclusion,” Alexander v. Louisiana, supra, 405 U.S. at 632, 92 S.Ct. at 1226, the assertions by the judges and Jury Commissioners of Orleans Parish are strongly corroborated by other evidence in the record. The 1960 *1129census figures introduced into evidence by Barksdale and summarized in the following table show that 70.8% of black males in Orleans Parish earned less than $3,000 per year, while only 35.9% of the white population earned this little; 93.6% of black men had annual incomes of $4,999 or less, compared with 59.5% of whites.
Total Number With No Income or With Income of $2,999 or Less Percent Number With No Income or With Income of $4,999 or Less Percent
Black Males, 14 and Over 76,222 53,944 70.8 71,339 93.6
White Males, 14 and Over 202,283 72,668 35.9 120,272 59.5
Source: Bureau of the Census, 1960 Census of Population (Part 20, Louisiana), Table 133.
Thus, the assertions by the judge and jury commissioners that blacks were underrepresented because they requested to be excused for economic hardship cannot be dismissed as mere ad hoc rationalization designed to camouflage invidious discrimination.
The panel opinion dismissed the state’s explanations for the racial disparities as either unsupported by the record or foreclosed by this court’s opinion in Labat v. Bennett, supra. We emphatically disagree. As previously shown, use of statistics describing the educational level of prospective black jurors substantially reduces the disparity between eligible black jurors and those actually serving on Orleans Parish jury venires. Thus, the differing literacy levels of prospective white and black jurors cannot be dismissed as a partial explanation for reduced black jury participation. Furthermore, the Jury Commission’s practice of granting hardship excuses to prospective jurors cannot be dismissed as being itself unconstitutional. Labat v. Bennett, supra, is not applicable to the facts of this case. Labat held that the exclusion of all daily wage earners as a class from jury service violated the Constitution.29 Similarly, Thiel v. Southern Pacific Co., 328 U.S. 217, 66 S.Ct. 984, 90 L.Ed. 1181 (1946), is not analogous; in that case, as in Labat, the Jury Commission “deliberately and intentionally excluded from the jury lists all persons who work for a daily wage.” 328 U.S. at 221, 66 S.Ct. at 986. The district court in this case specifically found that the Jury Commission did not exclude the entire class of daily wage earners. The panel opinion and the litigants appear to agree that about one third of those who were called to appear before the Jury Commission were black, so there was no discrimination at that stage.30 Then, in personal appearance before the Commission members, the uncontroverted evidence is that workers were excused for economic hardship only on request. Neither Labat nor Thiel can be read so as to proscribe the benign, and in many cases certainly beneficent, practice of excusing *1130from jury service those persons on whom it would impose an intolerable economic burden. “It is clear that a federal judge would be justified in excusing a daily wage earner for whom jury service would entail an undue financial hardship.” Thiel v. Southern Pacific Co., supra, 328 U.S. at 224, 66 S.Ct. at 987. See also 28 U.S.C. § 1863 (permitting excuses for “undue hardship”).
VII. Conclusion
The district court did not err in finding that the petitioner, Bruce Barksdale, failed to prove a prima facie case of jury discrimination. Clearly Barksdale failed to prove his case. A fair and reasonable assessment of the statistics shows disparities far too low to support a finding of jury discrimination. Moreover, the rebuttal evidence is valid and clearly demonstrates that the disparities found are not attributable to racial discrimination. Accordingly, the decision of the district court denying the writ of habeas corpus is
AFFIRMED.
STATISTICAL APPENDIX
I. 1960 POPULATION — ORLEANS PARISH
Source: 1960 Census, Part 20 (Louisiana) [hereinafter “1960 Census”], Table 20 & Table 96
Nonwhite males: 50,412
Percentage of nonwhites estimated to be non-black (from Table 96; assumes that same percentage of nonwhites who are nonblack in ages 20-64 applies for ages 21-64): 1.1%
Estimated black, male population aged 21-64 (50,412 reduced by 1.1%) 49,857
Total Male Population, ages 21-64 154,621
Black Percentage: 32.2%
II. OCCUPATIONALLY EXEMPT POPULATION, PERCENTAGE_
Source: 1960 Census, Tables 20,122.
Occupation Total White Black
Judges and Lawyers 1475 1471 4
Physicians and Surgeons 1515 1464 24
II. OCCUPATIONALLY EXEMPT POPULATION, PERCENTAGE
Source: 1960 Census, Tables 20, 122.
Occupation Total White Black
College Presidents, Professors, etc. 883 836 43
Dentists 380 363 17
Pharmacists 443 384 54
Firemen 996 996 0
Teachers 1453 992 531
TOTAL 7145 6436 673
Total Male Population, Ages 21-64 214,039 156,577 56,830*
Percent Exempt 3.34% 4.11% 1.18%
III. YEARS OF SCHOOL COMPLETED
Source: Levine Report, Tables 5-8
SEVENTH GRADE
Total White Nonwhite Black *
Males 25-64 106,573 79,850 26,723 26,429
Males 21-64, in school 2,826 2,319 507 501
Males 21-64, not in school 10,347 6,420 3,927 3,884
TOTAL 119,746 88,589 31,157 30,814
SIXTH GRADE
Total White Nonwhite Black*
Males 25-64 115,187 84,389 30,798 30,459
Males 21-64, in school 2,866 2,347 519 513
Males 21-64, not in school 10,771 6,601 4,170 4,124
TOTAL 128,824 93,337 35,487 35,096
IV. RACIAL BREAKDOWN OF THOSE ELIGIBLE . FOR JURY SERVICE_
Source: Tables above
SEVENTH SIXTH GRADE GRADE
Total Black Total Black
Males 21 64 119,746 30,814 128,824 35,487
Percent Exempt by Occupation 3.34% 1.18% 3.34% 1.18%
*1131IV. RACIAL BREAKDOWN OF THOSE ELIGIBLE FOR JURY SERVICE_
Source: Tables above
SEVENTH SIXTH GRADE GRADE
Total Black Total Black
Number Not Exempt 115,746 30,450 124,521 35,068
Percent of Eligibles Who Are Black 26.31% 28,16%
. Barksdale’s petition alleged that “[t]he State of Louisiana and the Parish of Orleans practiced a systematic exclusion of all but a token number of Negroes from the grand jury which returned the indictment charging petitioner with aggravated rape.” Additionally, he alleged that “[t]he State of Louisiana and the Parish of Orleans practiced a systematic exclusion of all but a token number of Negroes from the petit jury venire from which were selected the jurors who tried petitioner and who rendered the verdict of guilty as charged.”
. The following recital of the facts of Barks-dale’s crime was taken from the transcript of testimony before the state criminal trial court, which was included as an exhibit to this habeas petition.
. Labat v. Bennett, 365 F.2d 698, 729 (5th Cir. 1966) (Gewin, J., dissenting).
. Barksdale’s entire statement is reproduced in the dissent to the original panel opinion in this case. United States ex rel. Barksdale v. Blackburn, supra, 610 F.2d at 273-74 n. 2 (Ainsworth, J., dissenting).
. Daniel A. Knowles, Chairman of the Orleans Parish Jury Commission, testified in general regarding the construction of various jury lists, the qualification process for prospective jurors, and the procedure utilized in developing final grand and petit jury venires. There was also substantial discussion as to what information Knowles could obtain from his files regarding the racial characteristics of the jury selection process. Knowles did eventually supply information from which Barksdale and the state extracted a series of statistical stipulations.
The seven judges who testified stated that they did not intentionally exclude blacks from jury venires or grand juries, but that they affirmatively sought to avoid decreasing black representation on jury venires and panels. Virtually all of the judges testified that a disproportionately large number of blacks asked to be excused because of economic hardship.
. Barksdale pleaded not guilty and not guilty by reason of insanity. The insanity defense was never pursued at trial, however, and was withdrawn after closing arguments.
. The 1968 state habeas petition alleged systematic exclusion of blacks from the grand jury and petit jury venire. A later state habeas petition, also denied, was based on grounds not related to the present petition. State ex rel. Barksdale v. Henderson, 257 La. 551, 242 So.2d 886 (1971).
. The first hearing was held before Judge Christenberry, who died while the case was under consideration. A second evidentiary hearing was therefore held before Judge Schwartz; he denied that petition. Barksdale moved for a new hearing because of a factual error contained in Judge Schwartz’s opinion, and the state, which introduced the error through its brief, did not oppose the motion.
. Friendly, Is Innocence Irrelevant? Collateral Attack on Criminal Judgments, 38 U.Chi.L.Rev. 142 (1970).
. Another preliminary issue, suggested in a supplemental brief filed by Barksdale but not relied upon at oral argument, is whether the state is collaterally estopped from contesting the jury discrimination issue in light of Newman v. Henderson, 539 F.2d 502 (5th Cir. 1976). At one point, Barksdale’s habeas petition was consolidated for the purpose of an evidentiary hearing before a magistrate with that of John Newman, who alleged racial discrimination on the part of the same grand jury which indicted Barksdale. After the magistrate’s hearing, the cases were separated and sent back to different district judges. Newman’s conviction was eventually set aside by the Fifth Circuit.
In his brief, Barksdale relies heavily on Parklane Hosiery Co. v. Shore, 439 U.S. 322, 99 S.Ct. 645, 58 L.Ed.2d 552 (1979), a civil case which held that the mutuality doctrine did not bar application of collateral estoppel. “Under this mutuality doctrine, neither party could use a prior judgment as an estoppel against the other unless both parties were bound by the judgment.” Id., 439 U.S. at 326-27, 99 S.Ct. at 649 (footnotes omitted). Just last term, however, the Supreme Court held that nonmutual collateral estoppel cannot be used against the government in a criminal case. Standefer v. United States, 447 U.S. 10, 20-25, 100 S.Ct. 1999, 2006-08, 64 L.Ed.2d 689 (1980). While Standefer is not fully dispositive of the issue in a habeas corpus case, it would certainly be anomalous to maintain that nonmutual collateral estoppel does not apply at trial or direct appeal, but can be invoked on the very same issue in a habeas proceeding. In this case, as in Standefer, “[t]he public interest in the accuracy and justice of criminal results is greater than the concern for judicial economy professed in civil cases____” Standefer v. United States, supra, 447 U.S. at 25, 100 S.Ct. at 2008 (quoting from the Court of Appeals opinion). The other policy basis for estoppel— “protecting litigants from the burden of relitigating an identical issue” — carries little weight when a party not involved in the earlier judgment seeks to use estoppel offensively. Parklane Hosiery Co. v. Shore, supra, 439 U.S. at 326, 99 S.Ct. at 649. In Parklane Hosiery, the Supreme Court emphasized that courts should have “broad discretion to determine when [offensive collateral estoppel] should apply.” 439 U.S. at 331, 99 S.Ct. at 651. It was not an abuse of that discretion to deny application in this case. Collateral estoppel is appropriate only when the identical issue was fully litigated in the prior case. Here, the issue is whether the jury selection system discriminated against blacks. In Newman, the state contended first that Newman had waived any discrimination claim by failing to object at trial and, later, that the federal court should have relied on state findings rather than hold its own evidentiary hearing. Newman v. Henderson, supra, 539 F.2d at 504. As this court noted, “the state does not attack the finding of the district court that there was a systematic exclusion of qualified citizens from the grand jury that indicted Newman.” Id. Barksdale cannot now offensively use those unattacked findings.
. For example, in this case the general population of Orleans Parish in 1963 was found by the district court to be 39.5% black. The male population aged 21-64 in the same period was 34.4% black, substantially lower.
. Chief Justice Burger, dissenting in Castaneda v. Partida, supra, 430 U.S. at 504, 97 S.Ct. at 1285, wrote that “[tjhe decisions of this Court suggest, and common sense demands, that eligible population statistics, not gross population figures, provide the relevant starting point.” (emphasis in original)
. The panel majority opinion criticized the state for changing “its explanation of the statistics between the time it proposed findings of fact to the district court and the filing of its brief in this court.” 610 F.2d at 256. The state, on the basis of the 1960 census, did indeed urge in its appellate brief a view of the statistics more favorable to its case than those adopted by the district court. The state’s position in this regard is clear — it was defending the district court’s denial of habeas corpus relief, and in order to demonstrate the reasonableness of that result, the state attempted to demonstrate that there was a more supportive view available in the record.
. The disparity between eligible black males with at least seven years of education (26.2%) and the stipulated final petit jury venire for 1963 (21.86%).
. The disparity between the general black population in 1963 (39.5%) and the percentage of blacks on the 1964 grand jury venire as calculated by the panel majority (14.0%).
. Women were not compelled to serve on juries but could volunteer for jury service by filing written declarations of desire to serve. L.S.A.-R.S. 15:172.1.
. The qualifications and exemptions from jury service were established in L.S.A.-R.S. 15:172, 174:
§ 172. Qualifications
The qualifications to serve as a grand juror or a petit juror in any of the courts of this state shall be as follows:
To be a citizen of this state, not less than twenty-one years of age, a bona-fide resident of the parish in and for which the court is holden, for one year next preceding such service, able to read and write the English language, not under interdiction or charged with any offense, or convicted at any time of any felony, provided that there shall be no distinction made on account of race, color, or previous condition of servitude; and provided further, that the district judge shall have discretion to decide upon the competency of jurors in particular cases where from physical infirmity or from relationship, or other causes, the person may be, in the opinion of the judge, incompetent to sit upon the trial of any particular case.
In addition to the foregoing, jurors shall be persons of well known good character and standing in the community.
§ 174. Persons exempt from jury service
The following persons shall be exempt from serving as grand or petit jurors, but the exemption shall be personal to them and when they do not themselves claim exemption, it shall not be sufficient cause for challenging any person exempt under the provisions of this article:
(3) Judges and active officers of the several courts of this state, attorneys-at-law, physicians, surgeons, and dentists actively engaged in the practice of their profession and duly licensed under the laws of this state, professors and school teachers, school bus drivers, apothecaries, and all members of paid fire departments, and all commercial travelers, residing in the state who are actually engaged in travelling, either for themselves or in the interest of wholesale dealers, commission merchants or manufacturers.
(4) All persons over sixty-five years of age, those who from sickness or other physical *1125infirmity may be incapacitated from rendering such service, and those who have served as grand jurors under the provisions of this article during the previous six months, and those who have served as petit jurors as herein provided, who shall not again be called as jurors until the expiration of one year from the date of their service.
(5) All telegraph and telephone operators and railroad station agents. Also chief engineers of electric and water works systems.
. The formula for the Three-Point LeGrangian Interpolation is set out in the panel opinion, 610 F.2d at 226 n.20.
. No claim has been made that the use of the city directory itself is discriminatory.
. The decennial census is normally counted as of April 1 of the year, although recounting and refinement of the count continues for some time thereafter. See generally Preface, 1960 Census of Population (Part 20, Louisiana) at iii; see also Young v. Klutznick, 497 F.Supp. 1318 (E.D.Mich.1980).
. It might, in fact, be statistically sounder practice not to adjust for these exemptions at all since, by statute, they are “personal” and need not be taken. Some of the exempt group would likely be paid by their employer if they served and would be interested in serving.
. L.S.A.-R.S. 15:194 required that jurors have “the qualifications requisite to register as voters.” L.S.A.-R.S. 18:31 required that voters “understand the duties and obligations of citizenship under a republican form of government.” It is interesting to note that under *1126federal voting rights law, a sixth-grade education is required to create a presumption of literacy. 42 U.S.C. § 1971(c).
. These percentages were calculated using figures from Tables 4, 7, and 8 of the report of Dr. A. Levine, Barksdale’s expert witness (Plaintiffs Exhibit B), and Table 96 of the 1960 Census. See the statistical appendix, supra, for the exact calculations.
. The stipulation states in pertinent part:
23. According to the return to the Subpoena Duces Tecum issued to the Jury Commission out of 607 names in the jury wheel as of January 1, 1962, 118 or 19.43% were Negroes.
A. Note that the figure 118 includes a category called indeterminate in which there were 34 persons.
The Louisiana Supreme Court adopted the 19.43% figure in its opinion. 170 So.2d at 382. This figure may be questioned because of the presumption that all undetermineds were black, and we therefore also recalculate the percentage by assuming that 50% of the undetermined were black.
. Apparently the most common reason for not being able to determine race was that many people filled in the blank for race on their jury subpoena with the letter “C.” At one point in the pretrial hearing on the motion to quash the indictment, Barksdale’s attorney requested “the court to take judicial cognizance that when ‘C’ is used it is for colored. ... Of course, any cards in the file that had a ‘C’ would indicate that that meant colored.... Any white person is not going to take a chance and put a ‘C’ on his card.” State Court Record, Vol. II, Defendant’s Exhibit D-8, at page 175.
. The stipulation is contained in Volume 3 of the Record on Appeal at R-378.
Trial stipulation which assumed all persons of undetermined race were black.
Trial stipulation adjusted to assume that only 50% of persons of undetermined race were black.
. This stipulation is contained in Volume 5 of the Record on Appeal, at pages 921-24. It was designated “Stipulation D” by the district court.
. The number of blacks on each grand jury from September 1958 to September 1962 was as follows: 2, 2, 2, 2, 1, 2, 2, 2, 2.
. Since we decide that the present case is not governed by Labat, we need not address the appellant’s contention that Labat should not be given retroactive effect.
. The district court concluded that not all wage earners were excluded in part on the basis of its own sample: “Although the Court did not canvas [sic] the entire [city] directory, a reading of just the ‘A’s’ reveals twenty-eight ‘wage-earners’ who were sent notices for jury duty.” (footnote omitted)
Nonwhite population in Table 20, reduced by 1.1% to adjust for proportion of nonwhites who are nonblack.
Nonwhite population reduced by 1.1% to adjust for proportion of nonwhites who are nonblack.