DeMOSS, Circuit Judge:
Petitioner Ivan Ray Murphy appeals the district court’s denial of his petition for writ of habeas corpus under 28 U.S.C. § 2254. For the reasons set forth below, we affirm.
I. FACTUAL AND PROCEDURAL HISTORY
On the night of January 9, 1989, Petitioner Murphy and Douglas Stoff went to the home of Lula Mae Denning in Denison, Texas. Ms. Denning, an eighty-year-old lifetime friend of Murphy’s, invited the two men into her home. Once inside, the two men robbed Ms. Denning of jewelry, beat her to unconsciousness, and left her for dead. They returned several hours later to steal more jewelry that they could sell for more drugs.
A Grayson County Grand Jury indicted Murphy for the capital murder of Ms. Denning, specifically charging that he had committed murder during the course of the commission of a robbery or burglary. Following a trial, the jury returned a guilty verdict, and at a subsequent punishment hearing, the same jury answered affirmatively the two special issues set forth in the version of article 37.071 of the Texas Code of Criminal Procedure -that was in effect at the time of the offense. Accordingly, the trial court imposed upon Murphy the sentence of death.
Murphy’s conviction and sentence were automatically appealed to the Texas Court of Criminal Appeals. On September 23, 1993, in an unpublished opinion, that court affirmed Murphy’s conviction and sentence. And on October 11, 1994, the United States Supreme Court denied Murphy’s petition for writ of certiorari.
See Murphy v. Texas,
513 U.S. 926, 115 S.Ct. 312, 130 L.Ed.2d 275 (1994).
Murphy next filed an application for state habeas relief. The same judge who had presided over Murphy’s trial considered his application and issued a one-page order stating that there were no unresolved factual issues and recommending that Murphy’s application be denied. On February 28, 1996, the Texas Court of Criminal Appeals denied Murphy’s application for state habeas corpus relief.
Murphy then filed his petition for habeas corpus relief in federal district court asserting eleven claims for review. Following the district court’s denial of his petition, Murphy received from the district court, pursuant to 28 U.S.C. § 2253(c)(2), a certificate of appealability (“COA”) on the following two of eight issues for which he sought a COA: (1) whether the district court erred in refusing to grant Murphy’s request for discovery and an evidentiary hearing; and (2) whether the district court erred in denying Murphy’s claim that the grand jury selection process of Grayson County, Texas, violated his Sixth and Fourteenth Amendment rights. Murphy moved this Court for a COA on four of the six issues that had been denied by the district court. On March 8, 1999, a panel of this Court denied his request for an additional COA. With the benefit of briefing and the oral argument of counsel, we now proceed to the disposition of the original two issues for which a COA was granted by the district court.
II. DISCUSSION
Murphy’s petition for writ of habeas corpus was filed on December 16, 1996, and is thus governed by the provisions of the Antiterrorism and Effective Death Penalty Act (“AEDPA”).
See Lindh v. Murphy,
521 U.S. 320, 117 S.Ct. 2059, 2068, 138 L.Ed.2d 481 (1997);
United States v. Carter,
117 F.3d 262 (5th Cir.1997). The post-AEDPA version of 28 U.S.C. § 2254(d) provides as follows:
(d) An application for a writ of habeas corpus on behalf of a person in custody pursuant to the judgment of a State
court shall not be granted with respect to any claim that was adjudicated on the merits in State court proceedings unless the adjudication of the claim—
(1) resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States; or
(2) resulted in a decision that was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.
28 U.S.C. § 2254(d). We review pure questions of law under the “contrary to” standard of sub-section (d)(1), mixed question of law and fact under the “unreasonable application” standard of sub-section (d)(1), and pure questions of fact under the “unreasonable determination of facts” standard of sub-section (d)(2).
See Lamb v. Johnson,
179 F.3d 352, 356 (5th Cir.),
cert. denied,
— U.S. -, 120 S.Ct. 522, 145 L.Ed.2d 401 (1999) (citing
Drinkard v. Johnson,
97 F.3d 751, 767-69 (5th Cir.1996),
overruled in part on other grounds, Lindh v. Murphy,
521 U.S. 320, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997)).
An application of law to facts will only be deemed unreasonable when reasonable jurists “would be of one view that the state court ruling was incorrect.”
Drinkard,
97 F.3d at 769. Under this standard, we will grant habeas relief “only if a state court decision is so clearly incorrect that it would not be debatable among reasonable jurists.”
Id.
Additionally, under § 2254(e)(1), a state court’s determination of a factual issue must be presumed correct, and the habeas petitioner bears the burden of rebutting the presumption by clear and convincing evidence. The presumption is especially strong when, as here, the state habeas court and the trial court are one and the same.
See Amos v. Scott,
61 F.3d 333, 347 (5th Cir.1995);
James v. Collins,
987 F.2d 1116, 1122 (5th Cir.1993) (citing
Buxton v. Lynaugh,
879 F.2d 140, 146 (5th Cir.1989)).
As a preliminary matter, Murphy argues that his state court habeas petition was not “adjudicated on the merits” such that any presumption of correctness under § 2254(d) could apply to the state court’s findings. Our review of the record convinces us that both Murphy’s direct criminal appeal and his state habeas application were denied based upon a review of the merits of his claims. Thus, the standard set forth in 28 U.S.C. § 2254(d) applies to Murphy’s present claims.
A. Discovery and an Evidentiary Hearing
Murphy contends that the district court erred in two respects. First, he contends that it failed to grant his request for discovery regarding his claim of attorney misconduct arising from his allegation that the prosecutor induced a jailhouse informant to testify falsely and that the same prosecutor withheld
Brady
material. Second, Murphy contends that the district court improperly refused to grant his request for an evidentiary hearing based on the court’s conclusion that he had presented no factual issues that, if resolved in his favor, would entitle him to habeas corpus relief.
Discovery
Murphy asserts that the district court should have allowed him discovery to support his claims that the prosecutor improperly coerced a jailhouse informant, Michael McGregor, into testifying falsely against Murphy. Specifically, he wants to inspect and copy all documents, tapes, files, written reports, memoranda, notes, computer disks, or other written matter relating to the Grayson County Attorney’s investigation of the case. Murphy argues' that under
Bracy v. Gramley,
520 U.S. 899, 117 S.Ct. 1793, 138 L.Ed.2d 97 (1997), he is entitled to discovery to support his claims of prosecutorial misconduct. This court has already noted that the
Bracy
decision does not lower the gate for discovery in habeas cases, but rather it merely reasserts the standards of
Harris v. Nelson,
394 U.S. 286, 89 S.Ct. 1082, 22 L.Ed.2d 281 (1969). Thus, 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 ... entitled to relief, it is the duty of the courts to provide the necessary facilities and procedures for an adequate inquiry.”
Gibbs v. Johnson,
154 F.3d 253, 258 (5th Cir.1998),
cert. denied,
— U.S. -, 119 S.Ct. 1501, 143 L.Ed.2d 654 (1999).
The
Bracy
decision involved a defendant’s allegations that his judge was biased against him because the judge had been accused, and later convicted, of accepting bribes to fix murder trials. The Supreme Court noted that Bracy’s claims were framed in specific terms and were supported by objective, concrete factual evidence tending to support his theory (i.e., the subsequent conviction and other specific objective evidence). Good cause for discovery was established in
Bracy
based primarily upon the specific nature of the allegations and the concrete nature of the evidence proffered to support Bracy’s theory.
Rule 6 of the Rules Governing § 2254 cases permits discovery only if and only to the extent that the district court finds good cause. Good cause may be found when a petition for habeas corpus relief “establishes a prima facie claim for relief.”
Harris,
89 S.Ct. at 1086. Additionally, a petitioner’s factual allegations must be specific, as opposed to merely speculative or conclusory, to justify discovery under Rule 6.
See West v. Johnson,
92 F.3d 1385, 1399-1400 (5th Cir.1996) (citing
Ward v. Whitley,
21 F.3d 1355, 1367 (5th Cir.1994)). Simply put, Rule 6 does not authorize fishing expeditions.
See Ward,
21 F.3d at 1367.
Here, Murphy’s allegations of prosecutorial misconduct and the withholding of
Brady
material are insufficient to entitle him to discovery. Murphy has failed to establish a
prima facie
claim under
Brady
by virtue of his having failed to demonstrate the existence or concealment of a deal between the prosecution and the witness McGregor or that proof of such a deal would be material to the outcome.
Under
Brady,
a defendant’s due process rights may be violated when exculpatory or impeachment evidence, which is both favorable to the defendant and material to guilt or punishment, is concealed by the government.
See Hughes v. Johnson,
191 F.3d 607, 629 (5th Cir.1999). Evidence is material when there is a reasonable probability that a different outcome would have resulted if the government had disclosed the evidence prior to trial.
See id.
(citing
United States v. Bagley,
473 U.S. 667, 105 S.Ct. 3375, 3379, 87 L.Ed.2d 481 (1985)). Allegations that are merely “conclusion-ary” or are purely speculative cannot support a
Brady
claim.
See id.
at 629-30 (citing
United States v. Pretel,
939 F.2d 233, 240 (5th Cir.1991)).
After having carefully reviewed the entire record of this case, including all pleadings, transcripts, affidavits, and supplemental filings submitted to this Court, we conclude that Murphy’s conclusory allegation that the prosecutor failed to disclose a secret deal with McGregor is based purely on speculation. We find that the
Brady
materiality element is refuted by the fact that when cross-examined at trial, McGre-gor denied any deal, and by the defense’s introduction of the trial testimony of another inmate, Joseph Potts, who testified that McGregor wanted to get back at Murphy and also wanted to get out of jail at all costs. Murphy’s counsel argued his theory of a secret deal and all of these contentions vigorously to the jury which chose to reject them.
Because Murphy has pointed to little if anything which could be gleaned from additional discovery on this issue, and because by failing to establish a prima facie
Brady
claim he has failed to show good cause
for
discovery, we find that the dis
trict court did not err in denying Murphy additional discovery on this issue.
Evidentiary Hearing
Murphy also contends that the district court erred in failing to grant his request for an evidentiary hearing because the state courts summarily denied relief on his claims. He contends that there was no “adjudication” in the state court which would entitle the state court’s findings to a presumption of correctness. The government urges that the district court did not accord the presumption of correctness to the state court findings, rather it confined itself to the conclusion that Murphy alleged no facts which, if resolved in his favor, would entitle him to relief.
Under AEDPA, requests for an evidentiary hearing are to be evaluated under the provisions of 28 U.S.C. § 2254(e)(2).
See McDonald v. Johnson,
139 F.3d 1056, 1059 (5th Cir.1998). A habeas petitioner’s entitlement to an evidentiary hearing, when he has failed to develop the factual basis of a claim, is restricted to the narrow exceptions of subsection (e)(2) which provides as follows:
(2) If the applicant has failed to develop the factual basis of a claim in State court proceedings, the court shall not hold an evidentiary hearing on the claim unless the applicant shows that—
(A) the claim relies on—
(i) a new rule of constitutional law, made retroactive to cases on collateral review by the Supreme Court, that was previously unavailable; or
(ii) a factual predicate that could not have been previously discovered through the exercise of due diligence; and
(B) the facts underlying the claim would be sufficient to establish by clear and convincing evidence that but for constitutional error, no reasonable fact-finder would have found the applicant guilty of the underlying offense.
28 U.S.C. § 2254(e)(2). These exceptions are applicable only where the failure to develop the factual basis is the result of a decision or omission of the petitioner himself.
See McDonald,
139 F.3d at 1059.
Here, the government argues that under § 2254(e)(2) Murphy cannot be entitled to an evidentiary hearing because his claims aré not derived from any new rule of law from the Supreme Court, and because no new, previously undiscoverable facts establish his innocence of the crime. Indeed, as noted above, all of the evidence relied upon by Murphy to support his claim that the government had a deal with McGregor was available before, and was presented and argued at the original trial.
Murphy contends that he did not fail to develop the factual basis of his claims in state court, rather he argues that he was unable to do so because the state courts denied him discovery and an evidentiary hearing, and that as a result, § 2254(e)(2) does not automatically deny him the right to an evidentiary hearing in federal court. However, overcoming the narrow restrictions of § 2254(e)(2) does not guarantee a petitioner an evidentiary hearing, it merely opens the door for one; once a petitioner overcomes the obstacles of § 2254(e)(2), under Rule 8 of the Rules Governing § 2254 Cases, the district court retains discretion over the decision to grant an evidentiary hearing.
See McDonald,
139 F.3d at 1059-60. Thus, we review the district court’s denial of an evidentiary hearing in this scenario for an abuse of discretion.
See id.
at 1059.
Our pre-AEDPA jurisprudence is instructive in evaluating whether the district court’s denial of an evidentiary hearing was an abuse of discretion. Prior to the enactment of AEDPA, we consistently held that when there is a factual dispute which “ ‘if resolved in the petitioner’s favor, would entitle [the petitioner] to relief and the state has not afforded the petitioner a full and fair hearing,’ a federal habeas corpus petitioner is entitled to discovery and an evidentiary hearing.”
Perillo v. Johnson,
79 F.3d 441, 444 (5th Cir.1996) (quoting
Ward v. Whitley,
21 F.3d 1355, 1367 (5th Cir.1994));
see also Moawad v.
Anderson,
143 F.3d 942, 947-48 (5th Cir.),
cert. denied,
525 U.S. 952, 119 S.Ct. 383, 142 L.Ed.2d 316 (1998). To find an abuse of discretion that would entitle Murphy to an evidentiary hearing, we must find that the state did not provide him with a full and fair hearing and we must be convinced that if proven true, his allegations would entitle him to relief.
See Moawad,
143 F.3d at 948.
With respect to whether Murphy was afforded a full and fair hearing by the state court, Murphy contends that he requested discovery and an evidentiary hearing in the state habeas court, but that his requests were denied. The state habeas court then denied his application for habe-as relief based upon just those pleadings and affidavits that Murphy had submitted, without waiting for the government’s response and without holding a live eviden-tiary hearing, i.e. Murphy was given only a paper hearing,
see Perillo,
79 F.3d at 446 n. 7.
A full and fair hearing does not necessarily require live testimony. We have repeatedly found that a paper hearing is sufficient to afford a petitioner a full and fair hearing on the factual issues underlying his claims, especially where as here, the trial court and the state habeas court were one and the same.
See Perillo,
79 F.3d at 446-47 (listing cases where the presumption of correctness, which attached to factual determinations made after a full and fair hearing under the preAEDPA version of § 2254(d), was established with only a paper hearing before the same state judge who presided over the criminal trial). In his report and recommendation, the magistrate judge conceded that Murphy may arguably have been denied a full and fair hearing in the state court. We are not as convinced as the magistrate judge that Murphy was denied a full and fair hearing as the state habeas court, after first presiding over Murphy’s criminal trial and after considering the pleadings and affidavits that had been filed in support of Murphy’s claims, fully considered the merits of Murphy’s claims.
Additionally, while the numerous cases cited by Murphy do support the notion that a summary denial by a state court may entitle a petitioner to an evidentiary hearing in federal court, they overlook this court’s holding that, where a district court has before it sufficient facts to make an informed decision regarding the merits of a claim, a district court does not abuse its discretion in refusing to grant an eviden-tiary hearing (even where no factual findings are explicitly made by any state court).
See McDonald,
139 F.3d at 1060 (denying evidentiary hearing where state courts had failed to make any specific factual findings because the district court had sufficient affidavits from the parties in interest to make a determination). Here, the magistrate judge and the district court reviewed the record, pleadings, and all available evidence, including exhibits and affidavits in support of Murphy’s alleged claims. Furthermore, the magistrate judge recognized that Murphy arguably may not have been allowed a full and fair hearing in the state court, but nonetheless determined that the fact that Murphy failed to demonstrate a factual dispute that would entitle him to relief if it were resolved in his favor, justified denial of an evidentiary hearing.
We next consider whether there is a factual dispute that, if resolved in Murphy’s favor, would entitle him to relief. This Court has consistently held that a petitioner is entitled to an evidentiary hearing only where a factual dispute, if resolved in his favor, would entitle him to relief, and not where a petitioner’s allegations are merely conclusory allegations unsupported by specifics.
See Ward,
21 F.3d at 1367.
Murphy alleges that there was an undisclosed secret deal between the prosecutor and McGregor, but that he needs more discovery and an evidentiary hearing in order to fully develop this claim. His request in this regard is tantamount to an impermissible fishing expedition.
See Perillo,
79 F.3d at 444 (noting that Rule 6 of
the Rules Governing § 2254 Cases “ ‘does not authorize fishing expeditions.’ ” (quoting
Ward,
21 F.3d at 1367)). Discovery may only be permitted with respect to a specifically alleged factual dispute, not to a general allegation.
See Ward,
21 F.3d at 1367.
Here, Murphy’s claim was adequately developed below and Murphy has failed to demonstrate anything more than was presented and argued to the jury at trial. He seeks discovery and an evidentiary hearing in the hopes of finding additional evidence which might support his conclusory and speculative claim, but not with respect to a specific factual allegation which would entitle him to relief. As we have already noted, the discovery provisions of Rule 6 do not contemplate this type of fishing expedition. We therefore find that Murphy’s conclusory allegations are insufficient to require either discovery or an evidentiary hearing, and the district court did not abuse its discretion in denying Murphy’s request for the same.
B. Grand Jury Selection in Grayson County
In this second issue, Murphy contends that the grand jury selection process in Grayson County systematically excludes young people in violation of his Sixth Amendment right to an impartial jury and his Fourteenth Amendment right to equal protection. He correctly notes that the Sixth Amendment has been construed to require a petit jury to be drawn from a fair cross-section of the community in which the proceedings are held.
See Taylor v. Louisiana,
419 U.S. 522, 95 S.Ct. 692, 42 L.Ed.2d 690 (1975). He argues that the fair cross-section requirement applies to grand juries as well.
See Atwell v. Blackburn,
800 F.2d 502 (5th Cir.1986). However, as the government notes,
Atwell
does not specifically so hold. In fact,-the
Atwell
court in a footnote stated “[w]e do not hold that Atwell had a right ... to a grand jury selected under cross-sectional procedures similar to those implicated by the Sixth Amendment.”
Atwell,
800 F.2d at 507 n. 10. In
Atwell,
we assumed ar-guendo that if Atwell did have the right to a grand jury in conformance with the cross-sectional requirements of the Sixth Amendment, that right was not violated in his case.
The government argues first that at the time Murphy’s conviction became final in 1994, no Supreme Court authority dictated a rule that the fair cross-section requirement applies to state grand juries. The government suggests that the Sixth Amendment cross-section argument advanced by Murphy does not apply retroactively to his grand jury because, under
Teague v. Lane,
489 U.S. 288, 109 S.Ct. 1060, 103 L.Ed.2d 334 (1989), none of the appropriate exceptions to the non-retroactive applicability of the grand jury cross-sectional requirement apply.
We are not as convinced as the government that the fair cross-section requirement of the Sixth Amendment did not apply to Murphy’s grand jury, however, we are persuaded that
Teague
bars our consideration of Murphy’s claim that the fair cross-section requirement was violated by the alleged systematic exclusion of young people by the grand jury selection process in Grayson County.
Under
Teague,
we are prohibited from granting habeas relief based on “new” rules of constitutional law. A rule of constitutional law is “new” under
Teague,
if the result sought by application of the rule was not “dictated by precedent existing at the time the defendant’s conviction became final.”
Teague,
109 S.Ct. at 1070. Our duty is to “[s]urve[y] the legal landscape as it then existed and determine whether a state court considering [Murphy’s] claim at the time his conviction became final would have felt compelled by existing precedent to conclude that the rule [sought to be applied] was required by the Constitution.”
Caspari v. Bohlen,
510 U.S. 383, 114 S.Ct. 948, 953, 127 L.Ed.2d 236 (1994)(internal quotations and citations omitted). The only exceptions to the nonretroactivity principle of
Teague
are “for rules that would place certain primary con
duct beyond the government’s power to proscribe or bedrock rules of criminal procedure that are necessary to ensure a fundamentally fair trial.”
Felder v. Johnson,
180 F.3d 206, 211 (5th Cir.) (citing
O’Dell v. Netherland,
521 U.S. 151, 117 S.Ct. 1969, 1973, 138 L.Ed.2d 351 (1997)),
cert. denied,
— U.S. -, 120 S.Ct. 630, 145 L.Ed.2d 630 (1999).
Murphy’s conviction and sentence became final for purposes of our
Teague
analysis on October 11, 1994, when the Supreme Court denied his petition for certiorari after his conviction was affirmed on direct review in the Texas Court of Criminal Appeals.
See Murphy v. Texas,
513 U.S. 926, 115 S.Ct. 312, 130 L.Ed.2d 275 (1994). We have, therefore, limited our analysis to a survey of the legal landscape as it existed on October 11,1994.
The government urges that when Murphy’s conviction became final, there existed no precedent establishing a defendant’s right to a grand jury selected in conformance with the Sixth Amendment’s fair cross-section requirement. While in
At-well,
we declined to explicitly hold that Atwell had a right to a grand jury which represented a fair cross-section of the community, our earlier decisions are more specific. In
Curry v. Estelle,
524 F.2d 981 (5th Cir.1975), relying on the Supreme Court’s then recent decision in
Taylor v. Louisiana,
419 U.S. 522, 95 S.Ct. 692, 42 L.Ed.2d 690 (1975), we held that if a defendant could establish that a grand jury pool systematically excluding a substantial and identifiable class of citizens did not represent a fair cross-section of the community, his conviction was subject to attack.
See Curry,
524 F.2d at 983. We note additionally, that by October 1994, the Supreme Court had consistently held that racial discrimination in the selection of grand juries was violative of the fair cross-section requirement.
See Peters v. Kiff,
407 U.S. 493, 92 S.Ct. 2163, 2168, 33 L.Ed.2d 83 (1972);
Smith v. Texas,
311 U.S. 128, 61 S.Ct. 164, 166, 85 L.Ed. 84 (1940). Thus, at the time Murphy’s conviction became final, our precedent dictated that the fair cross-section requirement of the Sixth Amendment applied to the selection process for grand juries.
Despite the foregoing, Murphy’s burden under
Teague,
is to show that the particular result he desires was dictated by a particular precedent, that is, he must show that at the time his conviction became final, there existed precedent which would have compelled the state court to conclude that he was entitled to a grand jury comprised of a fair cross-section of the community with respect to certain age groups, more specifically, one which represented 18 to 30 year olds. In the absence of specific binding precedent prohibiting the exclusion of a specific group of individuals as violative of the fair cross-section requirement of the Sixth Amendment,
Teague
prohibits us from granting relief.
See, e.g., Wilkerson v. Whitley,
28 F.3d 498, 508 (5th Cir.1994)(en banc) (finding meritless, in light of the standard of proving that a result is dictated by particular precedent, the claim that cases prohibiting the exclusion of blacks from the grand jury selection process dictated the conclusion that the systematic exclusion of women from grand juries was unconstitutional).
While Murphy argues that the systematic exclusion of young people, ages 18 to 30 years old, from the grand jury selection process in Grayson County is unconstitutional because it violates the fair cross-section requirement, he has identified no precedent setting forth such a rule, and we have found none so specific. Thus, any declaration by this Court that the fair cross-section requirement of the Sixth Amendment is violated by the systematic exclusion of a group of individuals identified by their age, and any corollary finding that a grand jury selection process so excluding a specific age group is unconstitutional, would effectively announce a “new” rule of constitutional law. Under
Teague,
we are precluded from applying such a “new rule” to Murphy’s case unless he satisfies one of the two exceptions noted above. We conclude that neither of
the narrow exceptions to the
Teague
bar apply in this case. Having been referred to none, and having found no case dictating the result Murphy seeks, and having concluded that neither of the narrow exceptions to the
Teague
non-retroactivity principle apply, we are prohibited from granting the relief Murphy seeks in this issue. For similar reasons, we conclude that Murphy’s alternative claim that Gray-son County’s grand jury selection process violates his Fourteenth Amendment right to equal protection is likewise
Teague
barred.
III. CONCLUSION
For all of the reasons set forth above, we are unconvinced that the district court erred in refusing to grant Murphy either discovery or an evidentiary hearing, and we are precluded by the non-retroactivity principle announced in
Teague v. Lane
from granting relief on Murphy’s claims that the grand jury selection process in Grayson County, Texas, is violative of his rights under the Sixth or Fourteenth Amendments. Accordingly, we AFFIRM the district court’s denial of habeas corpus relief under 28 U.S.C. § 2254.