POLITZ, Chief Judge:

Kenneth Bernard Harris, sentenced to death by lethal injection for the murder of Lisa Stonestreet, seeks a certificate of probable cause to appeal the district court’s dismissal of his petition for writ of habeas corpus and for an order staying his execution presently set for April 25, 1996. We decline to issue the requested certificate and decline to order a stay.

BACKGROUND

On June 9, 1986 the police discovered the body of Lisa Stonestreet in the bathroom of her apartment in Houston, Texas, nude except for a pair of socks and a segment of pantyhose tied around her left wrist. Her body was draped over the side of the bathtub with her knees and feet on the floor and her head emersed in water in the bathtub.

Stonestreet’s apartment was in near total disarray. The investigating officers found a steak knife in her bedroom bearing a latent fingerprint matching Harris’ left index finger. Several pubic hairs found on her body matched Harris’ pubic hair. An autopsy revealed that Stonestreet had been beaten with a blunt instrument, that her wrists had been tightly bound, and that she had been manually strangled and drowned. Sperm was found in her vagina and rectum. The autopsy disclosed no damage to the anal sphincter, a finding consistent with anal intercourse after relaxation resulting from unconsciousness or death.

Early in the investigation of the homicide the authorities interviewed Harris who lived, with his girlfriend, in the next apartment. Harris then told the authorities that he did not know Stonestreet but that he had noticed a suspicious black pickup truck near the apartment complex a week before her death. On July 16, 1986, in its investigation of a recently burned vehicle belonging to Stone-street, the authorities found a palm print matching Harris’ right palm.

Harris was arrested for Stonestreet’s murder on July 22, 1986. After receiving Miranda warnings, Harris requested and was given permission to speak with his father. After doing so, Harris gave several statements, confessing that he strangled Stone-street after having consensual sex with her. He expressed remorse for the homicide, claiming that he was under the influence of drugs at the time.

Indicted for the capital murder of Stone-street, Harris was tried before a state jury in Harris County, Texas. The trial lasted four and one-half months, from August 17,1987 to January 4, 1988, and resulted in Harris’ conviction for capital murder. The sentencing phase extended from January 5,1988 to January 22, 1988. Harris presented evidence about his low intellectual capacity and his childhood experiences. In addition to offer *538 ing psychiatric evidence, the state called five women who testified that they had been victims of sexual assaults by Harris. These unadjudicated offenses occurred between December 10, 1985 and May 3, 1986, approximately six months and one month, respectively, before Stonestreet’s murder. At the conclusion of the sentencing phase the jury affirmatively answered the two special issues posed to it and the trial court sentenced Harris to death by lethal injection. Harris appealed his conviction and sentence to the Texas Court of Criminal Appeals which abated the appeal and remanded for the limited purpose of an additional Batson hearing. The appellate court concluded that the trial judge had erred, under controlling state precedent, by precluding defense counsel from cross-examining the prosecutor about the submitted race-neutral reasons for the exercise of peremptory strikes of four black members of the jury venire.

The trial court scheduled a hearing, as directed by the remand order, for January 30, 1992. Harris’ counsel appeared but informed the court that he was not ready to proceed because some of Harris’ files had been lost. The trial court granted counsel additional time to locate or reconstruct his files, informing counsel that the record would be returned to the Court of Criminal Appeals on February 27, 1992 unless prior thereto he notified the court that he was ready to proceed. Counsel did not so inform the court and, as advised, the record was returned to the Court of Criminal Appeals which affirmed Harris’ conviction and sentence. 1 Harris filed a petition for writ of certiorari which was denied. 2

On Harris’ state petition for writ of habeas corpus, the trial court of conviction entered detailed findings of fact and conclusions of law and recommended denial of the writ. 3 The Court of Criminal Appeals accepted that recommendation. 4 Harris then filed the instant petition under 28 U.S.C. § 2254, and moved for a stay of execution, discovery, and an evidentiary hearing. The respondent moved for summary judgment. The district court granted a stay of execution. It then considered and denied the motions for discovery and for an evidentiary hearing. After a full and thorough review of the state court record the district court granted the respondent’s motion for summary judgment, dismissed the writ application, lifted its order staying execution, and denied Harris’ motion for a certificate of probable cause to appeal. Harris now seeks from this court a certificate of probable cause and a stay of the execution presently set for April 25, 1996.

ANALYSIS

A. Certificate of Probable Cause

We have no jurisdiction over Harris’ appeal absent a CPC. 5 To obtain a CPC, Harris must make a substantial showing of the denial of a federal right. 6 “This standard does not require petitioner to show that he would prevail on the merits, but does require him to show the issues presented are debatable among jurists of reason.” 7 Further, in a capital case we properly may consider the nature of the penalty in deciding whether to grant a CPC but, as we have observed, that fact alone does not suffice to justify the issuance of a CPC. 8

B. Penry Claim

Harris claims that the two special issues posed did not permit the jury to make *539 the mandated reasoned moral response to the mitigating evidence about his mental capacity. 9 To support his Penry claim Harris relies on the testimony of Dr. Priscilla Ray, a forensic psychiatrist, who testified that Harris fell in the borderline defective or mildly defective range, as well as the testimony of Dr. Albert Smith, a clinical psychologist who similarly testified that Harris was “functioning in the borderline range of mental ability.” In addition to this expert testimony, Harris relies on various lay witnesses to establish his difficulty in learning. In its consideration of the Penry claim, the district court relied on the state trial judge’s factual findings in the state habeas proceedings that Harris’ IQ was estimated at different times to be 68, 71, and 93.

As we recently noted:

The first inquiry in a Penry claim is whether the mitigating evidence is relevant. Phrased differently, does the evidence implicate the basic concern of Penry that defendants who commit criminal acts that are attributable to a disadvantaged background, or to emotional and mental problems, may be less culpable than defendants who have no such excuse. ... In order to present relevant evidence that one is less culpable for his crime, the evidence must show (1) a uniquely severe permanent handicap with which the defendant is burdened through no fault of his own, ... and (2) that the criminal act was attributable to this severe permanent condition. 10

Assuming arguendo that Harris’ borderline intelligence constituted the type of uniquely severe permanent handicap required, his claim fails for lack of nexus between the mitigating evidence and the criminal act. 11 Our review of the record reflects the absence of any such evidence.

C. Batson Claim

Harris maintains that the district court erred in granting summary judgment on his claim that the state’s use of four of its peremptory challenges to strike African-Americans violated the holding of Batson v. Kentucky, 12 Summary judgment is appropriate if the record is devoid of a genuine issue of material fact. 13 In making this determination, we consider the facts contained in the summary judgment record, and the reasonable inferences to be drawn therefrom, in the light most favorable to the non-movant. In applying this standard, however, we are mindful that a federal court must accept as correct a state court’s findings of fact unless one of the 28 U.S.C. § 2264(d) exceptions apply. 14

Harris contends that a genuine issue of material fact exists herein as to whether the prosecution peremptorily released from the jury venire Dawnella Swan, Gloria Paul, An *540 thony Hackett, and Cornine Charles because of their race. Applying the mandated presumption of correctness, the district court did not err in its grant of summary judgment on this claim. The record abundantly supports the finding that the peremptory strikes were prompted by considerations other than race. In each instance the prosecutor provided, and the court accepted, race-neutral reasons which were supported by the voir dire record. The voir dire examination consumed more than three times as many trial days as did the trial on the merits.

D.Ineffective Assistance Claim

Harris maintains that defense counsel rendered constitutionally ineffective assistance in the handling of the Batson issue. Specifically, Harris contends that if counsel had cross-examined the prosecutor on the remand of the Batson issue, the challenge would have been successful. To prevail on this constitutional claim, Harris must establish that his counsel’s performance was deficient 15 and that such deficient performance prejudiced his defense. 16 To establish prejudice Harris must demonstrate a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceedings would have been different. 17 Moreover, he must establish that counsel’s errors rendered his trial fundamentally unfair or unreliable. 18

As previously alluded to, the trial record reveals detailed questioning during the voir dire of the prospective jurors, by both the prosecutor and defense counsel. The record also contains lengthy argument by the prosecutor and defense counsel on each of the challenged strikes. We perceive no reasonable probability that counsel’s cross-examination of the prosecutor would have produced a different result.

E. Discovery and Evidentiary Hearing

Harris next maintains that the court á quo erred by failing to permit discovery and for not conducting an evidentiary hearing on the Batson and ineffective assistance of counsel claims. When there is a factual dispute which, if resolved in the petitioner’s favor, would warrant relief, and the state court has not afforded the petitioner a full and fair evidentiary hearing, a federal habe-as petitioner typically is entitled to discovery and an evidentiary hearing. 19 Rule 6 of the Federal Rules Governing Section 2254 Cases does not, however, authorize fishing expeditions. A habeas petitioner must make sufficiently specific, factual allegations; con-clusionary allegations will not suffice to mandate either discovery or a hearing. 20 The record contains no factual allegations which, if fully developed, would have entitled Harris to relief on either claim.

F. Unadjudicated Offenses

Harris claims that the admission of the unadjudicated extraneous offenses during the sentencing phase of his trial violated the eighth amendment as well as the due process and equal protection clauses of the fourteenth amendment. Harris first contends that the admission of such offenses violates due process because the evidence under *541 mines the reliability of the decision to impose the death penalty. He then contends that the state must prove the unadjudicated extraneous offenses beyond a reasonable doubt. Finally, he maintains that the admission of the unadjudicated offenses during a capital sentencing hearing violates equal protection because extraneous unadjudicated offenses may not be introduced in the trials of defendants convicted of non-capital murder.

These submissions are not persuasive; they would require the announcement and application of a new rule contrary to the holding of Teague v. Lane 21 We previously have held that the use of evidence of unadjudicated extraneous offenses, at the sentencing phase of Texas capital murder trials, does not implicate constitutional concerns. 22 The authorities do not support Harris’ claim that the Constitution requires that the state prove unadjudicated offenses beyond a reasonable doubt before they may be used during the sentencing phase. Fully aware that the due process clause clearly requires that for conviction the state must prove the elements of the offense charged beyond a reasonable doubt, 23 neither we nor the Supreme Court has stated that a similar burden exists regarding the admission of evidence of unadjudicated offenses in a capital case sentencing hearing. 24

Finally, Harris’ equal protection challenge founders. Assuming arguendo that capital defendants and non-capital defendants are similarly situated, a parallel of which we are not persuaded, any disparate treatment would be rationally related to the state’s legitimate interest in assuring that all relevant information is presented for consideration by a capital jury in the discharge of its onerous obligation. 25

The motions for a certificate of probable cause and for a stay of execution are DENIED.

Notes

. Harris v. State, 827 S.W.2d 949 (Tex.Crim.App.1992).

. Harris v. Texas, 506 U.S. 942, 113 S.Ct. 381, 121 L.Ed.2d 292 (1992).

. Ex Parte Harris, No. 454652-A.

. Ex Parte Harris, No. 454652-A (Tex.Crim.App.1995).

. Fed.R.App.P. 22(b); Montoya v. Collins, 988 F.2d 11 (5th Cir.), cert. denied, 507 U.S. 1002, 113 S.Ct. 1630, 123 L.Ed.2d 263 (1993).

. Barefoot v. Estelle, 463 U.S. 880, 103 S.Ct. 3383, 77 L.Ed.2d 1090 (1983).

. Drew v. Collins, 5 F.3d 93, 95 (5th Cir.1993), cert. denied, -U.S. -, 114 S.Ct. 1207, 127 L.Ed.2d 555 (1994) (citing Barefoot, 463 U.S. at 893 n. 4, 103 S.Ct. at 3394 n. 4).

. Jacobs v. Scott, 31 F.3d 1319 (5th Cir.1994) (citations omitted), cert. denied, - U.S. -, 115 S.Ct. 711, 130 L.Ed.2d 618 (1995).

. Penry v. Lynaugh, 492 U.S. 302, 109 S.Ct. 2934, 106 L.Ed.2d 256 (1989).

. Davis v. Scott, 51 F.3d 457, 460 (5th Cir.) (internal quotations and citations omitted), cert. denied, — U.S.-, 116 S.Ct. 525, 133 L.Ed.2d 432 (1995).

. Id. At oral argument counsel vigorously contended that a nexus is inherent between any evidence of mental retardation and a crime, thus obviating a need for any additional showing. Our precedents require otherwise. See e.g., Ail-ridge v. Scott, 41 F.3d 213 (5th Cir.1994), cert. denied, — U.S. -, 115 S.Ct. 1959, 131 L.Ed.2d 851 (1995); Lackey v. Scott, 28 F.3d 486 (5th Cir.1994), cert. denied - U.S. -, 115 S.Ct. 743, 130 L.Ed.2d 644 (1995); Madden v. Collins, 18 F.3d 304 (5th Cir.1994), cert. denied, -U.S.-, 115 S.Ct. 1114, 130 L.Ed.2d 1078 (1995).

. 476 U.S. 79, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986).

. Williams v. Scott, 35 F.3d 159 (5th Cir.1994), cert. denied, - U.S. -, 115 S.Ct. 959, 130 L.Ed.2d 901 (1995).

. 28 U.S.C. § 2254(d). Counsel for Harris contends that the district court erroneously presumed the correctness of the state trial court's findings that the strikes were not racially motivated, vigorously submitting that: the state’s factfinding procedure was inadequate to afford a full and fair hearing; the material facts were not developed adequately; and he did not receive a full, fair, and adequate hearing in the state habe-as proceeding. Harris rests these assertions on the state habeas court’s denial of his motion for discovery. Whereas a state court’s refusal to permit discovery in some instances may support a conclusion that the state hearing was not full and fair, e.g., Moore v. Kemp, 809 F.2d 702 (11th Cir.), cert. denied, 481 U.S. 1054, 107 S.Ct. 2192, 95 L.Ed.2d 847 (1987), that is not the situation in the case at bar.

. In making this determination, we consider the particular circumstances of the case, viewed from counsel's perspective, in light of the then prevailing professional norms, in order to discern whether counsel’s performance fell below an objective standard of reasonableness. Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984).

. Harris contends that prejudice should be presumed herein based on United States v. Cronic, 466 U.S. 648, 104 S.Ct. 2039, 80 L.Ed.2d 657 (1984). We do not agree.

. Strickland.

. Lockhart v. Fretwell, 506 U.S. 364, 113 S.Ct. 838, 122 L.Ed.2d 180 (1993).

. Ward v. Whitley, 21 F.3d 1355 (5th Cir.1994), cert. denied, -U.S. -, 115 S.Ct. 1257, 131 L.Ed.2d 137 (1995). Rule 6 of the Federal Rules Governing Section 2254 Cases expressly provides for discovery in habeas proceedings if the petitioner shows “good cause.” The commentary to Rule 6 states:

Where specific allegations before the court show reason to believe that the petitioner may, if the facts are fully developed, be able to demonstrate that he is confined illegally and is therefore entitled to relief, it is the duty of the court to provide the necessary facilities and procedures for an adequate inquiry.

. Perillo v. Johnson, 79 F.3d 441 (5th Cir.1996).

. 489 U.S. 288, 109 S.Ct. 1060, 103 L.Ed.2d 334(1989).

. Williams v. Lynaugh, 814 F.2d 205 (5th Cir.), cert. denied, 484 U.S. 935, 108 S.Ct. 311, 98 L.Ed.2d 270 (1987); Callins v. Collins, 998 F.2d 269 (5th Cir.1993), cert. denied, - U.S. -, 114 S.Ct. 1127, 127 L.Ed.2d 435 (1994).

. See McMillan v. Pennsylvania, 477 U.S. 79, 106 S.Ct. 2411, 91 L.Ed.2d 67 (1986); In re Winship, 397 U.S. 358, 90 S.Ct. 1068, 25 L.Ed.2d 368 (1970).

. Justice Marshall's dissent from a denial of certiorari in Williams v. Lynaugh, 484 U.S. 935, 108 S.Ct. 311, 98 L.Ed.2d 270 (Marshall, J., with whom Brennan, J. joins, dissenting), does not support Harris’ contention that Supreme Court precedent dictates such a holding.

. Williams.