In a proceeding in the District Court of Oklahoma County, State of Oklahoma, a jury convicted Robyn Leroy Parks of the first-degree murder of Abdullah Ibrahim, a Gulf gas station attendant, and the same jury, after further hearing, sentenced Parks to death. Parks’ conviction and sentence were affirmed on direct appeal by the Oklahoma Court of Criminal Appeals. Parks v. State, 651 P.2d 686 (Okla.Crim.App.1982), and the Supreme Court of the United States denied certiorari, Justice Brennan and Justice Marshall dissenting. Parks v. Oklahoma, 459 U.S. 1155, 103 S.Ct. 800, 74 L.Ed.2d 1003 (1983).
Parks then sought post-conviction relief in the state courts of Oklahoma. The state district court denied relief and the Oklahoma Court of Criminal Appeals affirmed in an unreported order and opinion. Thereafter, the United States Supreme Court denied certiorari. Parks v. Oklahoma, 467 U.S. 1210, 104 S.Ct. 2400, 81 L.Ed.2d 356 (1984).
On June 29, 1984, eleven days before he was scheduled for execution, Parks filed in the United States District Court for the Western District of Oklahoma a petition for a writ of habeas corpus pursuant to 28 U.S.C. § 2254. The district court stayed execution, and, on November 5, 1985, in a 33-page opinion, dismissed all of the claims asserted by Parks in his petition except the claim of ineffective assistance of counsel at the penalty phase of the state criminal proceeding. Before ordering an evidentiary hearing concerning the claim of ineffective assistance, the district court determined to first propound interrogatories to the petitioner, Parks. Based on the answers thereto, the district court, by order of February 28, 1986, denied relief on the claim of ineffectiveness of counsel and dismissed all claims. This appeal followed. We are advised that the parties have agreed that no new execution date will be set pending disposition of the present appeal.
The government’s case-in-chief established the following. Abdullah Ibrahim, a native of Bangladesh, was attending school in Oklahoma and working part-time at a Gulf gas station in Oklahoma City, Oklahoma. On the morning of August 17,1977, a motorist who had stopped at the Gulf station at around 4:30 a.m. to buy some cigarettes found the attendant, Ibrahim, dead inside the station booth. Ibrahim’s death was caused by a gunshot wound in the chest. No money or other property had been taken from the booth. However, the investigating officers found an unused Gulf gas credit card charge slip in the booth with the letters and figures “XZ-5710” written on it and circled. The police checked out this alpha-numeric combination, and ascertained that it corresponded with the license number of an automobile in which Parks had an interest, possessory, at the least, if not strict legal title thereto.
Parks at this point in the investigation became either a prime suspect or a material witness, and it was ascertained that Parks was then in California. In the meantime the police had contacted a friend of Parks’, one James Clegg, and enlisted the latter’s aid. Clegg, in Oklahoma, called Parks, in California, on several occasions, and, with Clegg's consent, two phone conversations were tape recorded. In the first of these two recorded conversations, Parks told Clegg that he went to the Gulf station *1499intending to get gas with a stolen credit card and that the attendant came out of the booth and appeared to write down his license number. Fearing that the attendant would “call the law” and also fearful that if the police caught him they would find guns and dynamite which he had placed in the trunk of his car, Parks decided to kill the attendant so that if “he don’t be around there ain’t nothing he can tell them noway.” In this setting, according to Parks, he went to the station booth and shot and killed the attendant. Apparently, the door to the station booth was partially open and Parks fired one shot which struck Ibrahim in the chest.
In Parks’ second taped telephone conversation with Clegg, Parks, still in California, described where he had disposed of the murder weapon. Thereafter the police, accompanied by Clegg, went to the described location, which was miles away from the gas station, and recovered a .45 caliber revolver, together with a holster and ammunition, hidden under a bush. One shot had been fired from the revolver, the other five cylinders containing live ammunition. Parks was later arrested in California and extradited to Oklahoma. Both of the taped telephone conversations were played for the jury.
At trial, Parks testified in his own behalf and denied killing Ibrahim. He testified that at the time of the killing he was in another place, and a witness corroborated his alibi. Parks explained the fact that the license number of his car was found on the unused credit card slip by stating that several days before the homicide he had been in this particular gas station and had purchased gas when he had no money. He said the attendant at that time took down his license number, but that he had returned later on the same date and paid for the gas. Parks also explained his presence in California at the time of his arrest by testifying that subsequent to the date of the killing he had gone first to Kansas City, and then to California, in an effort to buy marijuana. On this general state of the record a jury convicted Parks of first-degree murder and the same jury, after further hearing, sentenced him to death.1
On appeal to this Court, Parks asserts that his state conviction and sentence is constitutionally infirm for any one, or all, of the following reasons: (1) failure of the state trial court to instruct the jury on a lesser included offense; (2) admission of a prior conviction of Parks for robbery by force and fear; (3) improper comment to the jury by the state prosecutor in the hearing at the penalty phase of the case; (4) error by the trial court in instructing the jury to disregard “sympathy”; (5) incomplete and misleading instruction on aggravating circumstances vis-a-vis mitigating circumstances; (6) ineffective assistance of counsel at the penalty phase hearing; and (7) failure of the trial court to hold an evidentiary hearing on his claim that Oklahoma’s death sentence statutes are applied in a racially discriminatory manner. These matters will be considered seriatim.
I. Lesser Included Offense
The state trial court refused to instruct the jury on murder in the second degree and such fact is alleged to render Parks’ conviction for first-degree murder unconstitutional. The state trial court initially refused to instruct on second-degree murder on the ground that “there was no evidence as to how much had been charged on the stolen card.” The trial court later grounded its refusal to thus instruct on the fact that there was “no evidence” that a credit card offense had been committed.2 The *1500Oklahoma Court of Criminal Appeals, on direct appeal, agreed that there was no evidence to support “a lower degree of the crime charged or an included offense....” Parks v. State, 651 P.2d, at 690.3
The federal district judge in the present habeas corpus proceeding was unimpressed with the reasoning of either the state trial court or the Oklahoma Court of Criminal Appeals on the lesser included offense argument, but nonetheless reached the same result based on Hopper v. Evans, 456 U.S. 605, 102 S.Ct. 2049, 72 L.Ed.2d 367 (1982) and Palmer v. State, 327 P.2d 722 (Okla.Crim.App.1958).4 In so holding, the federal district judge concluded that the state had made a prima facie case of the greater offense, i.e., murder in the first degree, and that the evidentiary matter relied on by the defendant, Parks, for requesting an instruction on second-degree murder was “no evidence whatever to refute the allegations of the information.” The court commented that, under Palmer v. State, supra, the evidence relied on by Parks, in order to justify the instruction on second-degree murder, must “raise the issue of whether the defendant was guilty of the lesser offense only.” We need not attempt to reconcile these different approaches to the problem, since our view of the testimony relied on by the defendant is such that there was no error in the trial court’s refusal to instruct on second-degree murder.
In advancing this particular argument, counsel relies heavily on Beck v. Alabama, 447 U.S. 625, 100 S.Ct. 2382, 65 L.Ed.2d 392 (1980). In Beck, the Supreme Court, citing Keeble v. United States, 412 U.S. 205, 93 S.Ct. 1993, 36 L.Ed.2d 844 (1973), commented, at p. 635, as follows:
In the federal courts, it has long been “beyond dispute that the defendant is entitled to an instruction on a lesser included offense if the evidence would permit a jury rationally to find him guilty of the lesser included offense and acquit him of the greater.” (Emphasis added).
Our analysis of the evidence relied on by counsel in advancing the lesser included offense argument is that the evidence would not permit a jury to rationally find Parks guilty of second-degree murder and acquit him of first-degree murder.
Under Oklahoma law, a person commits murder in the first degree when he unlawfully and with malice aforethought causes the death of another human being. Further, “malice” is defined as the “deliberate intention” to take the life of another, which intent is manifested by “external circumstances capable of proof.” Okla.Stat. tit. 21, § 701.7(A) (1981).
Okla.Stat. tit. 21, § 701.7(B) (1981) further provides that a person also commits the crime of murder in the first degree when he kills another, “regardless of malice,” in the commission of certain enumerated crimes, such as forcible rape, robbing with a dangerous weapon, kidnapping, and the like. A killing occurring in connection with the use of a stolen credit card is not one of the enumerated crimes constituting murder in the first degree.
Okla.Stat. tit. 21, § 701.8 (1981) provides that a homicide is murder in the second degree when perpetrated by an act imminently dangerous to another, “although without any premeditated design to effect. the death of any particular individual.” That same statute also states that a homi*1501cide is murder in the second degree when perpetrated by a person engaged in a felony “other than” the felonies enunciated in Okla.Stat. tit. 21, § 701.7(B) (1981). Okla. Stat. tit. 21, § 1550.22 (1981) provides, in effect, that it is a felony to unlawfully use or possess a stolen credit card.
Based on the foregoing statutes, Parks argues that under Oklahoma law the state district court should have instructed the jury on second-degree murder and that the failure to so instruct violates the mandate of Beck v. Alabama, supra. In thus arguing, counsel suggests that there is evidence that the homicide in the instant case occurred when Parks was engaged in a felony (using a stolen credit card) other than the ones enumerated in Okla.Stat. tit. 21, § 701.7(B) (1981) and that accordingly an instruction on second-degree murder was mandated by Beck. The argument borders on the ingenious, but in our view does not stand up under a careful analysis of the evidence relied on for the giving of such instruction.
As indicated, Parks testified in his own behalf and denied killing Ibrahim, testifying that he was elsewhere at the time of the homicide. So, there is nothing in the defendant’s testimony that would justify giving an instruction on second-degree murder. The evidence which counsel relies on in advancing the present argument are the statements made by the defendant to Clegg in the two tape-recorded telephone conversations, particularly the first of the two conversations. We do not agree that these statements made by Parks to Clegg required an instruction to the jury on second-degree murder.
Parks, in his statements to Clegg, indicated that he had gone to the Gulf station to buy gas with a “hot” credit card. Presumably, Parks had pumped the gas and had used the “hot” credit card for payment. In any event, thereafter Parks noticed the attendant taking down his license number. Then, Parks, according to his statements to Clegg, formed a deliberate intent to kill the attendant in the belief that “dead men tell no tales.” Parks at the time was apparently concerned not only with the “hot” credit card, but also with the small arsenal, consisting of guns and dynamite, which he had in the trunk of his car. It was in this setting that Parks proceeded to the attendant’s booth and, through the partially opened door to the booth, shot Ibrahim once in the chest. This evidence does not justify an instruction on a homicide without malice occurring in the use of a stolen credit card. It only shows a premeditated killing of another with deliberation and malice, the motive, therefore, being a desire to avoid possible detection by the police.
We believe our holding that the evidence in the instant case did not require an instruction to the jury on second-degree murder squares not only with Beck, but that it is also in accord with subsequent decisions of the Supreme Court in such cases as Hopper v. Evans, 456 U.S. 605, 102 S.Ct. 2049, 72 L.Ed.2d 367 (1982) and Spaziano v. Florida, 468 U.S. 447, 104 S.Ct. 3154, 82 L.Ed.2d 340 (1984). Hopper involved a homicide perpetrated during the course of an armed robbery. The defendant, against the advice of his attorney, testified and stated, in effect, that he deliberately shot the deceased in the back. Later, in a federal habeas corpus proceeding brought by the defendant’s mother, the Supreme Court held that an instruction on second-degree murder was not required since “the defendant’s own evidence negates the possibility that such an instruction might have been warranted.” 456 U.S., at 606, 102 S.Ct. at 2050. In the instant case, Parks’ own statements to Clegg concerning the homicide negate his counsel’s claim of second-degree murder.
In Spaziano v. Florida, supra, there apparently was evidence, which if believed by the jury, would have supported a verdict of second-degree murder. However, the Florida statute of limitations had run on murder in the second degree, a non-capital offense, but had not run on murder in the first degree, a capital offense. In such circumstance, the state trial judge refused to instruct the jury on second-degree murder unless the defendant agreed to waive the statute of limitations. This the defend*1502ant refused to do, and no instruction was given. The defendant was ultimately convicted of first-degree murder and sentenced to death. The Supreme Court in Spaziano found no error in the state trial court’s refusal to instruct on second-degree murder, stating that “[w]here no lesser included offense exists, a lesser included offense instruction detracts from, rather than enhances, the rationality of the process. Beck does not require that result.” 468 U.S., at 455, 104 S.Ct. at 3159.
II. Admission of Evidence That Parks Had a Prior Felony Conviction
In 1972, Parks, then seventeen years of age, was charged as an adult with robbery by force and fear. He pled guilty to the charge and was given a five-year suspended sentence. A few years later Parks was also convicted of attempted burglary in the second degree after a felony charge and was imprisoned for three years for that conviction. At the very commencement of the state trial on the murder charge, Parks sought an order which would preclude the use of his prior conviction for robbery at the guilt phase of the proceeding. No challenge was made to the prosecution’s possible use of the burglary conviction for impeachment purposes should Parks elect to testify in his own behalf. The reason advanced for the exclusion of the robbery conviction was that Parks was only seventeen years of age at the time of the robbery conviction and that accordingly such conviction was invalid under Lamb v. Brown, 456 F.2d 18 (10th Cir.1972). See Radcliff v. Anderson, 509 F.2d 1093 (10th Cir.1974) (en banc), cert. denied, 421 U.S. 939, 95 S.Ct. 1667, 44 L.Ed.2d 95 (1975); Bromley v. Crisp, 561 F.2d 1351 (10th Cir.1977) (en banc), cert. denied, 435 U.S. 908, 98 S.Ct. 1458 (1978). See also Edwards v. State, 591 P.2d 313 (Okla.Crim.App.1979).
The state trial court denied Parks’ request, noting that no challenge had ever been made in state court to the conviction. At trial, then, defense counsel, in his direct examination of Parks in the “guilt-phase” of the state proceeding, brought out the fact of the robbery conviction and the burglary conviction. This was the state of the record on this particular matter when the case went to the jury on the guilt-or-innocence phase of the trial. Later, in the penalty phase of the bifurcated proceeding, the jury was ultimately apprised of all of the underlying facts leading up to Parks’ plea of guilty to robbery with force or fear. In brief, the facts were that Parks, and two other black youths, accosted a white student in a school yard and after a fight took six cents from the victim. All involved were students.
The federal district judge in the habeas corpus proceeding ruled that any possible error in connection with the admission into evidence of Parks’ prior robbery conviction was, when viewed in context, “harmless error” as that term is defined in Chapman v. California, 386 U.S. 18, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967). We agree and are not inclined to disturb that ruling.
At the time when the jury was deliberating the guilt-or-innocence of Parks on the murder charge, the jurors knew about the robbery conviction, but did not, at that time, know of the underlying facts leading up to Parks’ plea of guilty to the robbery charge.5 However, counsel in the penalty phase of the proceeding went “behind” the robbery conviction and apprised the jury of all the underlying facts and circumstances. Thus, the jury was eventually fully informed about the entire matter and knew that this was not, by way of example, the armed robbery of a bank by an adult offender, but, on the contrary, arose out of a fracas in a school yard where only six cents was taken from the pocket of the victim.
In our view, this entire episode was de minimis, and must have been viewed as such by the jury. As the federal district court observed, the evidence of Parks’ guilt *1503was overwhelming. It is seldom that authorities have a tape-recorded confession to a crime made during the investigative process. In the first tape-recorded telephone conversation, Parks admitted the crime and related details which only the perpetrator could know. In the second recorded conversation, Parks detailed where the death weapon could be found, and the police, following Parks’ directions, found the weapon. The introduction of the robbery conviction at the guilt phase of the proceedings is plainly harmless error, if it be error, beyond any reasonable doubt.
In the penalty phase of the proceeding, where the jury was weighing life vis-a-vis death, the jury was fully informed as to the circumstances giving rise to the robbery charge. At that stage, the jury in effect rejected the State’s arguments for the sole statutory aggravating circumstance to which this robbery conviction was relevant, when it refused to find that there was a probability that Parks would commit criminal acts of violence in the future that would constitute a continuing threat to society. See note 1, supra. The only aggravating circumstance contended for by the State which the jury found supported by the evidence was that the murder was committed by Parks for the purpose of avoiding or preventing a lawful arrest or prosecution, which was the reason given by Parks himself for the killing. We refuse to believe that a jury would impose the death sentence because of Parks’ conviction for a crime arising out of a school yard fist fight. To us, it is inconceivable that a jury of twelve adults would be influenced in any manner by such testimony to the end that such would affect their deliberation on either the question of guilt or penalty in a first-degree murder proceeding. We have more faith in the jury system.
III. Improper Comment by State Prosecutor in Closing Argument
Counsel argues that statements made by the prosecutor to the jury during closing argument in the penalty phase of the case come within the prohibitions laid down in Caldwell v. Mississippi, 472 U.S. 320, 105 S.Ct. 2633, 86 L.Ed.2d 231 (1985). The Supreme Court in Caldwell held that it is “constitutionally impermissible to rest a death sentence on a determination made by a sentencer who has been led to believe that the responsibility for determining the appropriateness of the defendant’s death rests elsewhere.” Id., at 328-29, 105 S.Ct. at 2639 (emphasis added). In Caldwell, the prosecutor, according to the majority opinion, sought to “minimize the jury’s sense of the importance of its role.” Specifically, the state prosecutor commented that should the jury return a death sentence, such would be “automatically reviewable by the Supreme Court.”
In the instant case, the state prosecutor spoke to the jury as follows:
But, you know, as you as jurors, you really, in assessing the death penalty, you’re not yourself putting Robyn Parks to death. You just have become a part of the criminal justice system that says when anyone does this, that he must suffer death. So all you’re doing is you’re just following the law, and what the law says, and on your verdict — once your verdict comes back in, the law takes over. The law does all of these things, so it’s not on your conscience. You’re just part of the criminal justice system that says when this type of type [sic] of thing happens, that whoever does such a horrible, atrocious thing must suffer death. Now that’s man’s law. But God’s law is the very same. God’s law says that the murderer shall suffer death. So don’t let it bother your conscience, you know.
We do not read the prosecutor’s comment to minimize the importance of the jury’s role in fixing Parks’ sentence. In Darden v. Wainwright, 477 U.S. 187, 106 S.Ct. 2464, 91 L.Ed.2d 144 (1986), the Supreme Court, in footnote 15 at page 2473, stated, in part, as follows:
Caldwell is relevant only to certain types of comment — those that mislead the jury as to its role in the sentencing process in a way that allows the jury to feel less responsible than it should for the sentencing decision. In this case, none of the comments could have had the effect *1504of misleading the jury into thinking that it had a reduced role in the sentencing process. If anything, the prosecutors’ comments would have had the tendency to increase the jury’s perception of its role. We therefore find petitioner’s Eighth Amendment argument unconvincing.
In Dutton v. Brown, 812 F.2d 593 (10th Cir.1987) (en banc), and in Coleman v. Brown, 802 F.2d 1227, 1240-41 (10th Cir.1986) this Court considered closing arguments quite similar, though not completely identical, to that made in the instant case and held that such comment was not constitutionally impermissible. In the instant case, we have read the entire closing argument of both the prosecutor and defense counsel in the penalty-phase of the case. There was no objection by defense counsel to the prosecution’s argument. We fail to see how the argument of the prosecution, read in its entirety, tends to minimize or downgrade the importance of the jury’s determination of the penalty to be imposed. Indeed, the prosecutor’s remarks tended to dramatize the extreme importance of the matter and was an exhortation to the jury to “follow the law” of both man and God.
IV. Anti-Sympathy Instruction
Instruction No. 9 at the penalty phase of the state proceeding advised the jury, in part, as follows:
You are the judges of the facts. The importance and worth of the evidence is for you to determine. You must avoid any influence of sympathy, sentiment, passion, prejudice or other arbitrary factor when imposing sentence. You should discharge your duties as jurors impartially, conscientiously and faithfully under your oaths and return such verdict as the evidence warrants when measured by these Instructions (emphasis added).
Trial counsel did not object to the foregoing instruction. However, counsel in the federal habeas corpus proceeding in the district court, and here, argues that the giving of the “anti-sympathy” instruction constitutes constitutional error. In thus arguing, counsel relies primarily on Skipper v. South Carolina, 476 U.S. 1, 106 S.Ct. 1669, 90 L.Ed.2d 1 (1986); Eddings v. Oklahoma, 455 U.S. 104, 102 S.Ct. 869, 71 L.Ed.2d 1 (1982); Lockett v. Ohio, 438 U.S. 586, 98 S.Ct. 2954, 57 L.Ed.2d 973 (1978); and, in a Supplemental Brief, counsel both relies on and distinguishes the recent case of California v. Brown, — U.S. -, 107 S.Ct. 837, 93 L.Ed.2d 934 (1987).
Neither Skipper, Eddings, nor Lockett concern an instruction to the jury that in their deliberations they should “avoid any influence of sympathy, sentiment, passion, prejudice or other arbitrary factor....” These cases all stand for the general proposition that under the Eighth and Fourteenth Amendments the sentencer in a capital case should not be precluded from considering as a mitigating factor any aspect of the defendant’s character and background which might serve as the basis for a sentence less than death. In Skipper, the Supreme Court held that the exclusion of testimony of jailers and of a regular visitor regarding the defendant’s good behavior during the defendant’s seven months’ incarceration in jail awaiting trial deprived him of his right to place before the sentencers “relevant evidence on mitigation.” In Eddings, the Supreme Court vacated a state conviction wherein the death penalty was imposed after the state court refused to consider as a mitigating circumstance the defendant’s unhappy upbringing and emotional disturbance, including evidence of the defendant’s turbulent family history and beatings by a harsh father. In Lockett, the Supreme Court held that “in all but the rarest kind of capital case, [the sentencer may] not be precluded from considering, as a mitigating factor, any aspect of a defendant’s character or record that the defendant proffers as a basis for a sentence less than death.” 438 U.S., at 604, 98 S.Ct. at 2964 (opinion of Burger, C.J.) (footnotes omitted) (emphasis in original).
In its simplest form, then, Parks’ argument is that “sympathy” could serve as the basis of a sentence less than death, and therefore the jury must be allowed to consider it. The Supreme Court recently con*1505fronted an “anti-sympathy” instruction in California v. Brown, supra. In that case, the jury was instructed not to be “swayed by mere sentiment, conjecture, sympathy, passion, prejudice, public opinion or public feeling” during the penalty phase. 107 S.Ct., at 840. The California Supreme Court had held that the anti-sympathy instruction violated the Eighth Amendment and stated that a defendant had a right to “sympathetic consideration of all the character and background evidence” which is presented as mitigating evidence. People v. Brown, 40 Cal.3d 512, 709 P.2d 440 (Cal.1985). The Supreme Court granted certio-rari and reversed, holding that the anti-sympathy instruction in Brown did not violate the Eighth or Fourteenth Amendments. It is true that the Supreme Court in Brown noted that the instruction there referred to “mere sentiment, conjecture, sympathy, passion, prejudice, public opinion or public feeling,” whereas the instruction in the instant case did not utilize the adjective “mere.” However, such, under Brown, does not dictate a reversal in the instant case, and, in any event, we are not persuaded by the rationale of the California Supreme Court in Brown.
In our view, “sympathy” and “mitigating factors” are not synonyms. Mitigating factors are based on evidence arising generally out of testimony concerning a defendant’s background and from the facts and circumstances surrounding the crime for which the defendant is on trial. Sympathy, on the other hand, as is evident from the context of the challenged instruction, here plainly refers to the mere emotional responses of jurors. The instruction directs the jury to make its sentencing decision based on the aggravating and mitigating evidence presented, and not on “extraneous emotional factors.” Brown, 107 S.Ct., at 840. A jury should indeed not be influenced by “sympathy” for either the defendant, or, for that matter, for the victim and his family.
In his Supplemental Brief in this Court, petitioner attempts to show that, under the approach of Justice O’Connor’s concurring opinion and four dissenters in Brown, the challenged instruction, taken together with certain remarks made by the prosecutor, renders his sentence infirm. In Brown, Justice O’Connor agreed that an anti-sympathy instruction, by itself, does not violate the Constitution. However, she cautioned that care must be taken, else “juries may be misled into believing that mitigating evidence about a defendant’s background or character also must be ignored.” 107 S.Ct., at 842 (concurring opinion). Here, however, there is no possibility that the jury was misled concerning its role or the scope of the mitigating circumstances it could consider. The jury was clearly informed that the only bound on the mitigating circumstances it could consider was the evidence found “to exist in this case.” 6 In addition to the statutory mitigating circumstances, which the jury was told it must consider, the court instructed the jury that it “may consider any other or additional mitigating circumstances, if any, that you may find from the evidence to exist in this case.”
Thus the jury was not instructed to ignore mitigating evidence. Such an instruction would indeed run afoul of the principles of Lockett and Eddings. Instead, the *1506jury was instructed to confine its consideration of both aggravating and mitigating factors to the evidence before it, to “avoid any influence of sympathy, sentiment, passion, prejudice, or other arbitrary factor when imposing sentence,” and to discharge its duties “impartially, conscientiously and faithfully under your oaths and return such verdict as the evidence warrants when measured by these Instructions.” Since we believe that a rational juror, hearing this instruction, would conclude “that it was meant to confine the jury’s deliberations to considerations arising from the evidence presented, both aggravating and mitigating,” Brown, 107 S.Ct., at 840, the petitioner’s claim based on the “anti-sympathy” instruction must be denied.
V. Incomplete and Misleading Instructions On Aggravating Circumstances Vis-a-vis Mitigating Circumstances
Instruction No. 7 given the jury, without objection, in the penalty-phase proceeding reads as follows:
In the event you find unanimously that one or more of these aggravating circumstances existed beyond a reasonable doubt, then you would be authorized to consider imposing a sentence of death.
If you do not find unanimously beyond a reasonable doubt one or more of the statutory aggravating circumstances existed, then you would not be authorized to consider the penalty of death, and the sentence would be imprisonment for life.
Even if you find unanimously one or more of the aggravating circumstances existed beyond a reasonable doubt, and if you further find that such aggravating circumstance or circumstances is outweighed by the finding of one or more mitigating circumstance, then and in such event the death penalty shall not be imposed, and the sentence would be imprisonment for life.
On appeal, Parks asserts that the foregoing instruction is constitutionally defective in three particulars: (1) the instruction failed to instruct the jury that even if it found that the aggravating circumstances outweighed the mitigating circumstances it could still impose a life sentence and, that the charge instructed the jury, inferentially at least, that if it found that the aggravating circumstances outweighed the mitigating circumstances it must impose the death penalty; (2) it improperly places a burden on the defendant of proving that mitigating circumstances outweigh the aggravating circumstances; and (3) it fails to adequately define the nature and function of mitigating circumstances. We do not agree.
Under the instruction set forth above, and in accord with Oklahoma statutory and case law, the jury was instructed that it must impose a life sentence unless it unanimously found beyond a reasonable doubt that one or more of the aggravating circumstances alleged by the state existed. Parks’ counsel does not object to this statement. The instruction goes on to advise the jury that even if it should find beyond a reasonable doubt the existence of one or more of the aggravating circumstances relied on by the state, it must still impose only a life sentence if it should further find that the aggravating circumstances are outweighed by the mitigating circumstances. Again, counsel has no objection to that part of the instruction. As indicated, what counsel does object to is that the instruction did not go further and instruct the jury, in just so many words, that even if it found that aggravating circumstances outweighed any mitigating circumstances, it could, in its discretion, still fix the penalty at life imprisonment. Such an instruction is not required under Oklahoma law. Nor is such, in our view, required by the Eighth and Fourteenth Amendments.
The first paragraph in the challenged instruction states that the jury is “authorized to consider imposing a sentence of death” if it finds unanimously that one or more of the statutory aggravating circumstances existed beyond a reasonable doubt. The second paragraph in the instruction is the reverse of the first paragraph, and instructs the jury that they are not authorized to consider the penalty of death if they do not find unanimously that one or more of the statutory aggravating circumstances existed beyond a reasonable *1507doubt. The third paragraph in the instruction instructs the jury that the death penalty cannot be imposed even if they find unanimously one or more of the statutory aggravating circumstances existed beyond a reasonable doubt, if the jury further finds that such aggravating circumstance, or circumstances, is, or are, outweighed by a further finding of one or more mitigating circumstances. The first paragraph speaks in terms of “authorized to consider” the death penalty, and is not directory in its terms. We think the instruction adequately advised the jury on this particular matter.
In Burrows v. State, 640 P.2d 533, 544 (Okl.Cr.1982), the Oklahoma Court of Criminal Appeals was faced with the same argument made here. In rejecting that argument, the Court spoke as follows:
The defendant’s twenty-first assignment of error is, in part, identical to the argument presented in our recent decision of Irvin v. State, 617 P.2d 588 (Okl.Cr.1980). Arguing from Laws 1976, 1st Extraordinary Session, Chapter 1, Section 5, now 21 O.S.Supp.1980, § 701.11, defendant claims that the jurors must be told four things prior to beginning deliberations. First, the death penalty cannot be imposed unless the jury finds one or more aggravating circumstances beyond a reasonable doubt; second, if the jury finds one or more aggravating circumstances, then they may consider imposing the death penalty; third, if the jury finds one or more aggravating circumstances, but the circumstances are outweighed by mitigating circumstances of the case, the jury cannot impose the death penalty; fourth, even if the jury finds aggravating circumstances, and those circumstances are not outweighed by mitigating circumstances, they can decline to impose the death penalty. In the defendant’s case, the jury was given the first three instructions but not the fourth. As in Irvin, the argument is rejected. The fourth instruction was subsumed in the second, since the jurors were told that they could, not that they had to, impose the death sentence. As stated in Irvin:
The only discretion provided the jury under the statute [21 O.S.Supp.1980, § 701.11] is that necessary to make a factual finding of the existence or nonexistence of aggravating and mitigating circumstances, as well as the discretion requisite in balancing the two.
We do not read the instruction set forth above as casting any burden of proof on the defendant. Under that instruction, the jury first had the responsibility of determining whether the state had proved beyond a reasonable doubt any of the aggravating circumstances set forth in its Bill of Particulars. If the jury so found, then, and only then, was it to “weigh” the aggravating circumstance thus found against the mitigating circumstances in the case. This, to us, is not a burden of proof matter.7
Further, in our view, the jury was adequately instructed on the nature and function of mitigating circumstances. Instruction No. 6 identified eight “mitigating circumstances,” and advised the jury that it was not limited to such itemization and could consider “other or additional mitigating circumstances, if any, you may find from the evidence to exist in this case.”8
*1508VI. Ineffective Assistance of Counsel In the Penalty Phase Proceeding
In the federal habeas corpus proceeding, counsel concedes that defense counsel in the state trial court competently and vigorously represented Parks in the guilt phase of Parks’ first-degree murder trial. However, it is argued here that Parks’ counsel thereafter, in effect, “threw in the towel” and that his representation of Parks in the penalty-phase proceeding was constitutionally deficient and that such prejudiced Parks and conceivably tipped the scales for the death penalty, instead of life imprisonment. The record does not support this argument.
Parks was represented in the state trial court by David Hood, who was retained by Parks’ father. We agree that Hood’s representation of Parks in the guilt phase of the case was not only constitutionally acceptable, but was, from our reading of the record made in the state trial proceeding, considerably above the norm. The jury returned its verdict of guilty at about five o’clock on a Friday afternoon. Hood and the prosecutor were both of a view to commence the penalty phase of the case immediately. The judge, however, thought the jury was perhaps “tired” and set the penalty phase hearing for eight o’clock a.m. on the next day. In the penalty phase hearing, all of the evidence adduced at the trial, which included all of the testimony of the defendant, Parks, was reintroduced. Hood then called as his only witness Parks’ father. Parks’ father testified at some length concerning his son, his home environment, his education and personal traits. The State had earlier indicated that it might not call any witnesses at the penalty-phase hearing, but after the father testified about his son’s robbery conviction, the State did call as a rebuttal witness the victim of the fracas in the schoolyard. The victim’s father also testified, and it would appear from his testimony that it was the father’s insistence which resulted in the filing of charges against Parks.
After closing argument, which was vigorous, the jury received the case around noon. After lunch, the jury commenced their deliberations around 1:30 p.m. and returned the death penalty around 4:45 p.m. At the request of Hood, who was of course present with Parks when the verdict was received, the jury was polled and all jurors indicated that they had voted for the death penalty.
In the hearing in federal district court, the judge initially denied all of Parks' claims for relief except the one claim of ineffective assistance of counsel. Rather than hold a full-scale evidentiary hearing into the ineffectiveness of counsel argument, the district court decided to first submit written interrogatories to Parks, which interrogatories Parks, in time, answered and thereafter filed supplemental answers thereto. Parks at this point in time was represented by local Oklahoma counsel who presumably assisted Parks in his answers to the interrogatories. Further, no objection was made at that time to using interrogatories as opposed to a full scale evidentiary hearing.
In any event, the answers indicated quite clearly that the sole basis for the claim of ineffectiveness of counsel was that Hood didn’t call more witnesses to testify concerning Parks’ personal history. In this court, Park’s counsel states that there were “at least 25 of Parks’ friends, relatives and associates who would have testified in his behalf,” and who “would have painted a more complete picture of him as a *1509human being, i.e., church attendance, good performance in school subjects, his non-violent nature as a youth,” and the like. It should be noted that by the time a claim of ineffective trial counsel was first made, David Hood, who was Parks’ trial counsel, was deceased, having died a short time after the trial. Be that as it may, based on Parks’ answers to the interrogatories, and upon a review of the record before him, which included a transcript of the state trial proceedings, the federal district judge rejected the claim of ineffective counsel. Under the circumstances, we are disinclined to disturb his ruling on the matter.
In Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), the Supreme Court held that in order to prevail on a claim of ineffective assistance of counsel, a defendant must demonstrate that “counsel’s representation fell below an objective standard of reasonableness,” id., at 688, 104 S.Ct. at 2064, and that “there is a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different.” Id., at 694, 104 S.Ct. at 2068. Thus, in order to grant relief, a reviewing court must find that both parts of the Strickland test are met. The reviewing court must “indulge a strong presumption” that counsel’s assistance was effective, and it is the defendant’s burden to overcome the presumption that “the challenged action ‘might be considered sound trial strategy.’ ” Id., at 689, 104 S.Ct. at 2065, quoting Michael v. Louisiana, 350 U.S. 91, 101, 76 S.Ct. 158, 164, 100 L.Ed. 83 (1955). In applying Strickland, we bear in mind that the “essence of an ineffective assistance claim is that counsel’s unprofessional errors so upset the adversarial balance between defense and prosecution that the trial was rendered unfair and the verdict rendered suspect.” Kimmelman v. Morrison, 477 U.S. 365, 106 S.Ct. 2574, 2583, 91 L.Ed.2d 305 (1986).
Applying these principles to the instant case, we agree with the federal district court that Parks cannot prevail on his claim of ineffective counsel. The fact that counsel did not call a succession of witnesses who would presumably testify concerning Parks’ boyhood years and testify generally as to his character does not show deficient performance by defense counsel. See Dutton v. Brown, 812 F.2d 593 (10th Cir.1987). Under the circumstances, deciding not to call character witnesses was perhaps a wise tactical move. Such witnesses would have been subject to cross-examination and rebuttal. Though Parks may have had an innocent boyhood, his more recent past was not so spotless. In addition to his plea of guilty to the robbery charge, Parks had also been convicted of burglary for which he had served time. Further, as mentioned above, Parks at the time of the homicide was apparently in the drug business. At least that was Parks’ own testimony at trial where he explained his presence in California at the time of his arrest by stating that he was in California on a “buying trip.” This aspect of the case, of course, was not fully explored in the guilt-phase proceeding, but no doubt defense counsel felt that if he tried at the penalty phase proceeding to inject Parks’ general character into the case, the state would endeavor to bring out all the details of Parks’ current endeavors, including his trafficking in drugs, as well as the guns and dynamite, which were apparently in the trunk of Parks’ vehicle, and the purpose for which they were intended.
Counsel argues here that at the very least Parks should have been given an evi-dentiary hearing on the claim of ineffective counsel and points out that there was an evidentiary hearing in Strickland. We do not believe, however, that an evidentiary hearing must be given in every case involving a claim of ineffectiveness of counsel. In the present case, defense counsel was not available to testify, having died shortly after the state trial. The federal district judge did not reject, out of hand, Parks’ claim that defense counsel’s courtroom performance was constitutionally deficient. He allowed Parks, assisted by his counsel, to answer interrogatories. And these answers, and supplemental answers, indicated quite clearly that the only fault he had with his counsel was his failure to place his entire history before the jury. If counsel *1510had placed before the jury the entire record made by Parks from the date of his birth to the date of trial, such would undoubtedly include Parks’ present drug activities, which would probably not have enhanced Parks’ position in the eyes of the jury. If such had been the scenario, the claim in the present proceeding would be that counsel was deficient in permitting his life history to go to the jury. In our view, defense counsel did a competent and vigorous representation of Parks throughout the entire trial. His arguments to the jury were impassioned. In the words of Strickland, Parks’ present claim of deficient representation is grounded on “the distorting effects of hindsight.” 466 U.S., at 689, 104 S.Ct. at 2065.
VII. Refusal of the Federal District Court To Hold an Evidentiary Hearing on Parks’ Claim That Oklahoma’s Death Penalty Statutes Are Applied Arbitrarily and Discriminatorily Against a Defendant Such as Himself Charged with Killing a White Victim
In his petition for habeas corpus, Parks urged as his ninth ground for relief that the application of the death sentence to his case violated his Eighth and Fourteenth Amendment rights. In his petition, Parks initially stated that his case is perhaps the only case where a death sentence was imposed solely on the aggravating circumstance that at the time of the homicide he was attempting to avoid arrest or detection, and that in 90% of the cases where a death sentence was imposed in Oklahoma the jury either found that the offense was heinous, atrocious and cruel, or that there was a probability that the defendant would constitute a continuing threat to society because of his record of violent misconduct, neither of which was the finding of the jury in his case. This particular reason apparently fell by the wayside and was not pursued in the district court, nor is it raised in this Court.
In his petition, and as a part of this ninth ground for relief, Parks also urged that based on a study by Samuel R. Gross, an Acting Associate Professor of Law at Stanford University, and Robert Mauro, an Assistant Professor of Psychology at the University of Oregon, one is more likely to receive the death penalty in Oklahoma if he has killed a white person than if he has killed a black person. In this connection, it is further alleged that Parks “will further bring out evidence of other forms of racial discrimination in Oklahoma County.” In support of this claim, Parks later proffered to the federal district court Professors Gross and Mauro’s study, since published as Patterns of Death: An Analysis of Racial Disparities in Capital Sentencing and Homicide Victimization, 37 Stan.L. Rev. 27 (1984) (the Gross-Mauro Study).
The federal district court declined to hold an evidentiary hearing on the claim of racial discrimination in the application of Oklahoma’s death penalty statutes. The judge was of the view that what may have happened in some other case didn't prove, or even tend to prove, what had occurred in Parks’ case.
The conclusion of the Gross-Mauro study is that it is the color of the victim, rather than the color of the defendant, that impels a jury to more readily return a death penalty vis-a-vis a life sentence. In the instant case, the victim, Abdullah Ibrahim, was a native of Bangladesh temporarily in the United States, and he is not white-skinned, but, from the photograph in the record before us, is very dark-skinned. Under such circumstances, a court would be going far afield to hold an evidentiary hearing on the basis of the Gross-Mauro study. A Bangladesh victim does not appear to fall into place in the Gross-Mauro study.9
Moreover, the Supreme Court recently considered and rejected a similar claim in McClesky v. Kemp, — U.S. -, 107 S.Ct. *15111756, 95 L.Ed.2d 262 (1987). In McClesky, a study similar to the Gross-Mauro study offered here was considered. That study (the Baldus study) purported to show a disparity in the imposition of the death penalty in the State there involved, Georgia, on the basis of the race of the murder victim.10 McClesky there argued, as Parks does here, that the statistical disparities shown by the proffered study demonstrated that Georgia’s capital punishment statute violated both the Equal Protection Clause of the Fourteenth Amendment and the Eighth Amendment’s ban on “cruel and unusual punishments.” See McClesky, 107 S.Ct., at 1770.
The Supreme Court rejected McClesky’s Equal Protection Clause argument. It held that in order to prevail on the equal protection claim, McClesky had to “prove that the decisionmakers in his case acted with discriminatory purpose.” McClesky, 107 S.Ct., at 1769 (emphasis in original). The Supreme Court examined the Baldus study and found it “clearly insufficient to support an inference that any of the decisionmak-ers ... acted with discriminatory purpose.” 11 The Supreme Court also rejected McClesky’s Eighth Amendment claim that his death sentence was excessive since racial considerations may have influenced capital sentencing decisions in Georgia. It found that at most, “the Baldus study indicates a discrepancy that appears to correlate with race,” id., at 1777, and refused to assume that the unexplained discrepancy resulted from invidious racial discrimination. The Gross-Mauro study proffered here is similar to the Baldus study considered in McClesky. Like the Baldus study, it does not show what transpired in Parks’ case. Nor does it demonstrate a “constitutionally significant risk” of racial discrimination.12
Parks has offered no evidence that would support an inference that the decision makers in his case acted with a discriminatory purpose. As indicated, such evidence is essential in order to prevail under the Equal Protection Clause. Parks’ Eighth Amendment claim must also fail. He has not demonstrated a “constitutionally significant risk of racial bias.” As the Supreme Court has observed, discrepancies in sentencing decisions appearing in studies such as the proffered Gross-Mauro study are but an inevitable part of our criminal justice system. See McClesky, supra, 107 S.Ct., at 1778.
Finally, the additional proffer by Parks that if given time he could “bring out evidence of other forms of racial discrimination in Oklahoma County” is conclusory and non-specific in nature, and did not require the district court to hold an evidentia-ry hearing. See Andrews v. Shulsen, 802 F.2d 1256, 1266 (10th Cir.1986) where we upheld a district court’s ruling that an evi-dentiary hearing was unnecessary where the allegations of discrimination in fact were conclusory, stating that a “habeas petitioner must provide supporting factual allegations.”
In sum, we think the defendant got a fair trial. Perhaps not a perfect one, but we know of no rule that in a capital case the trial must be perfect. Certainly there is nothing before us to indicate that the entire proceeding was fundamentally unfair, or that there has been a miscarriage of justice. Parks’ defense, as stated, was an alibi. The jury rejected that defense. Ac*1512cordingly, the facts and circumstances of the homicide, coming necessarily from only the state’s evidence, showed a senseless, cold-blooded killing, the evidence therefor coming from the defendant himself. And, as previously stated, defense counsel did all he could do with what he had to work with.
Judgment affirmed.
. At the penalty phase, the State sought three statutory aggravating circumstances. First, the State alleged that the murder was especially heinous, atrocious, or cruel. Second, the State alleged that the murder was committed for the purpose of avoiding or preventing lawful arrest or prosecution. Third, the State alleged the existence of a probability that the defendant would commit criminal acts of violence that would constitute a continuing threat to society. The jury found only the second statutory aggravating circumstance charged, i.e., that the murder was committed to avoid or prevent a lawful arrest or prosecution.
. The judge stated:
As a matter of fact, the defendant’s own testimony was that he didn’t even own a credit card. But even in the State's case there was no evidence of a credit card, except his state*1500ments and his statements alone do not prove the corpus delecti of the crime. There is no corpus delecti of any other felony having been committed. ... There is no evidence and, consequently, it’s Murder One or nothing.
. This holding is consistent with other pronouncements of the Oklahoma courts. See e.g., Irvin v. State, 617 P.2d 588, 596 (Okla.Crim.App.1980) (where no evidence supports requested second-degree murder instruction, unnecessary to instruct thereon); Seegars v. State, 655 P.2d 563 (Okla.Crim.App.1982).
. In Palmer v. State, 327 P.2d 722 (Okla.Crim.App.1958), the Oklahoma court held that it was not error to refuse to give a lesser included offense instruction where the state made out a prima facie case of the greater offense, and there was "no evidence whatever to refute the allegations of the information_” In order to justify or require the giving of a lesser included offense instruction, there must be “evidence sufficient to raise the issue_” 327 P.2d, at 726.
. Although the fact of the robbery conviction was admitted by Parks on direct examination, the conviction’s underlying facts were not presented to the jury at that time. On objection of the prosecutor, the state trial court ruled that Parks’ testimony regarding the circumstances surrounding the robbery conviction was incompetent at that stage. The prosecutor did not pursue the robbery conviction on cross-examination.
. With regard to nonstatutory mitigating circumstances, Parks' jury was instructed as follows:
You are not limited in your consideration to the minimum mitigating circumstances set out herein, and you may consider any other or additional mitigating circumstances, if any, that you may find from the evidence to exist in this case. What facts or evidence that may constitute an additional mitigating circumstance is for the jury to determine.
In Brown, the jury there was instructed that it could consider nonstatutory mitigating circumstances as follows:
Any other circumstance which extenuates the gravity of the crime even though it is not a legal excuse for the crime.
Justice O'Conner was concerned that the jury may have understood this instruction to limit its consideration of nonstatutory mitigating factors to evidence about the circumstances of the crime, and to preclude consideration of evidence about the defendant’s character and background. See Brown, 107 S.Ct., at 842 (concurring opinion). The instruction given here, however, does not so limit the jury’s consideration.
. The Supreme Court has stated that “specific standards for balancing aggravating against mitigating circumstances are not constitutionally required.” Zant v. Stephens, 462 U.S. 862, 875 n. 13, 103 S.Ct. 2733, 2742 n. 13, 77 L.Ed.2d 235 (1983). In Andrews v. Shulsen, 802 F.2d 1256 (10th Cir.1986), also a death penalty case, we recently observed that "sentencing authorities may determine a defendant’s fate without regard for burdens of proof or other measures of certainty.” 802 F.2d, at 1264. See abo Ford v. Strickland, 696 F.2d 804, 817-19 (5th Cir.1983) (opinion of Roney, J.) (burden of proof argument confuses proof of facts and weighing of facts in sentencing; weighing process not a fact susceptible of proof under any standard); Sonnier v. Maggio, 720 F.2d 401, 408 (5th Cir.1983), cert. denied, 465 U.S. 1051, 104 S.Ct. 1331, 79 L.Ed.2d 726 (1984); Foster v. Strickland, 707 F.2d 1339, 1345 (11th Cir.1983).
. We have examined the cases from other Circuits relied upon by the petitioner, and have determined that they do not support his position. See e.g. Peek v. Kemp, 784 F.2d 1479 (11th Cir.1986) (en banc), cert. denied, — U.S. -, 107 S.Ct. 421, 93 L.Ed.2d 371 (1986); Spivey v. Zant, 661 F.2d 464 (5th Cir. Unit B 1981), cert. denied, 458 U.S. 1111, 102 S.Ct. 3495, 73 L.Ed.2d *15081374 (1982). In Peek, the Eleventh Circuit held that the constitution requires only that there be "no reasonable possibility’ that a juror will fail to understand "the meaning and function of mitigating circumstances.” 784 F.2d, at 1494. In Andrews v. Shulsen, 802 F.2d 1256 (10th Cir.1986), we recently stated that sentencing instructions need only instruct the jury that "the law recognizes circumstances which may be considered as extenuating or otherwise reducing a defendant's culpability and hence his punishment.” 802 F.2d, at 1264. In the instant case, the state trial judge's instructions on mitigating circumstances were lengthy and thorough. The jurys attention was clearly focused on the possible existence of mitigating circumstances, and, in Instruction No. 7, the jury was instructed as to its role in the sentencing decision. There is no reasonable possibility that Parks’ jury failed to comprehend the nature and function of mitigating circumstances in reaching its decision.
. The Gross-Mauro study itself states that "cases involving Asian or American Indian defendants or victims have been removed from any tabulations that include the racial characteristics of the defendants or of the victims, respectively, from all regression analyses, and from tabulations involving our scale of aggravation." Patterns of Death, 37 Stan.L.Rev., at 52 (footnote omitted).
. The Baldus study also purported to show a disparity in the imposition of the death penalty based on the race of the defendant, although to a lesser extent. In contrast, the Gross-Mauro study here at issue indicates that, in Oklahoma, the race of the suspect did not have a statistically significant role in the imposition of the death penalty. See Patterns of Death, 37 Stan.L.Rev., at 97 n. 187.
. At an evidentiary hearing, McClesky’s expert witness testified that the Baldus study did not show what occurred in any given case. McClesky, 107 S.Ct., at 1767 n. 11.
.The Gross-Mauro study concluded that in Oklahoma, "the odds of receiving the death penalty for killing a white were 4.31 times greater than the odds of receiving the death penalty for killing a black.” Patterns of Death, 37 Stan.L. Rev., at 96 n. 184. This figure is substantially identical to that which the Supreme Court characterized as "not demonstrat[ing] a constitutionally significant risk of racial bias_" McClesky, 107 S.Ct., at 1767.