EMILIO M. GARZA,' Circuit Judge:
Joseph Roland Lave, Jr. (“Lave”) moves for a certificate of appealability (“COA”) to appeal the district court’s denial of his habeas petition under 28 U.S.C. § 2254. Specifically, he argues that reasonable jurists would find it debatable whether: 1) Lave’s Sixth Amendment rights were violated under a retroactive application of the Supreme Court’s decision in Crawford v. Washington, 541 U.S. 36, 124 S.Ct. 1354, 158 L.Ed.2d 177 (2004); 2) Lave was denied effective assistance of counsel; 3) the district court erred in denying Lave’s motion for limited discovery; and 4) the trial court violated Lave’s rights under the Fifth Amendment’s prohibition against double jeopardy. In addition, Lave contends that the district court abused its discretion by not allowing him to amend his federal petition or return to state court in order • to raise a Sixth Amendment Crawford claim.
I
Lave, James Langston (“Langston”), and Timothy Bates (“Bates”) conspired to rob a sporting goods store. During the robbery, the assailants brutally killed two of the store’s employees, Frederick Ban-zhaf (“Banzhaf’) and Justin Marquart (“Marquart”). A third employee, Angela King, was also attacked but managed to survive, call 911 and identify Langston as [376]*376one of the perpetrators. As a result of her identification, the police sought to apprehend Langston. During the attempted arrest, Langston tried to run over the police officers. The police responded by shooting Langston who died soon after. Inside Langston’s shoe, the police found a card with Bates’ name and phone number. Using that information, the police arrested Bates, who identified Lave as the third robber. Subsequently, the police executed a warrant and searched Lave’s apartment and automobile, where they seized merchandise from the sporting goods store and other evidence. Lave surrendered to the police two days later.
Lave was tried for the murder of Marq-uart. During the trial, the prosecution sought to present Bates’ testimonial evidence through Kevin Hughes (“Hughes”), the police officer who had taken Bates’ statement. Before calling Hughes to the stand, the prosecutor made the following statement to the court outside the presence of the jury:
I represented to the Defense last night that I believe that the state of the evidence now is that Mr. Lave killed all three people .... [I]f we rested with that evidence, the Jury would not hear the testimony of Bates, because we— I’ve represented to Mr. Franklin [defense counsel] that we feel we didn’t have to call Bates now, with the evidence being that way. I told Mr. Franklin that what I propose to do was to adduce the statements of Bates through Sergeant Hughes, much as we did at the last trial. At the last trial, it was — the State’s theory of that was that they were admissions against penal interest and Hughes could testify what Bates said under an admission against penal interest theory.
At the last trial, Mr. Franklin ... objected. I told them if they waived objection, what — what I propose to do is adduce the statements of Mr. Bates through Sergeant Hughes, and some salutary benefits would accrue to Mr. Lave. One, the statement of Bates takes, at least circumstantially, two of the — two of the attacks off Mr. Lave. If you’ll recall, the statement of — of Sergeant Hughes was that Bates said that he saw Langston hit one of the boys with a hammer. I would argue then on that evidence that — that Langston attacked the boys.
So that takes a least two of the assaults off Mr. Lave, that’s in his best interest. It was in my best interest, frankly, not to have to call Mr. Bates. I don’t want to have to sponsor him; I don’t want to deal with him. If I can try this case without having to cut a deal with Mr. Bates, I’d like to do that. I told the Defense if I called Bates, Bates would automatically get a life sentence; I would offer him that. I told them that even if I didn’t call him, he might get a life sentence. But I’m in a much better posture of dealing with Mr. Bates at arm’s length if I don’t have to call him.
So, that’s of some benefit to Mr. Lave, too, because if he gets the death sentence, I — I can’t see as he would want Mr. Bates to get a life sentence. So, I saw some benefits for both sides, the— the principal benefit being it takes a couple of the attacks off Mr. Lave and puts those on Langston. And the — the big benefit to us is that it puts those on Langston. And the the big benefit to us is that it puts a knife in Lave’s hands.
If you’ll remember, the statement of Bates is he saw Lave come out with a knife and turn it over to Langston. And Mr. Bates said Lave got the money and left with the money. So I saw both sides getting some benefit out of the statement of Bates being adduced through Sergeant Hughes. I would only do that though, if the Defense would waive objection.
[377]*377This morning, Mr. Franklin and I talked. I told him I wouldn’t call Bates if — if the agreement could be reached. He asked me what would happen if I called — if he called Mr. Lave to the stand. I said, “Well, in that case, I would call Mr. Bates in rebuttal, I anticipate,” and I think that’s where the matter is now.
I will represent to the Defense if — if that agreement is acceptable to them, where they achieve some benefit and I achieve some benefit, if we can adduce that statement of Bates from Sergeant Hughes without objection, then I do not intend and I will not call Bates in my case in chief, nor will I call him in rebuttal unless something happens from the Defense side that I feel, in good faith, would require Bates to be called— to counter something.
All I understand the Defense has as a defense is an alibi. And certainly, if — as I understand the defense, I wouldn’t anticipate nor would I call Bates to rebut an alibi. So, if that’s acceptable to y’all that’s what I offer to do.
Defense counsel and Lave both expressly agreed to the prosecution’s proposal. As a result, Sergeant Hughes took the stand and testified that Bates told him that, on the night of the crime, he and Langston went to the sporting goods store and met with Lave. Langston gave Lave a gun and the two of them went to the front and broke in. Bates waited in the back until his accomplices allowed him to enter. Hughes stated that Bates had told him that while waiting in the hallway he saw Lave in a room with Langston and that Langston was striking one of the victims with a hammer. When Bates saw this, he went outside to the back of the store and waited for his accomplices. Eventually, Lave, with Langston, emerged from the back carrying the knife and drove off with the money.
Lave did not testify. At the end of the trial, the jury convicted Lave for the murder of Marquart, under Texas’ law of the parties, and sentenced him to death. Lave appealed the verdict to the Texas Court of Criminal Appeals. The court affirmed, and Lave filed a petition for a writ of certiorari which the United States Supreme Court denied. Lave then filed an application for a writ of habeas corpus which was denied by the state trial court; that decision was affirmed by the Texas Court of Criminal Appeals.
Lave filed a petition for federal habeas relief with the United States District Court for the Northern District of Texas. The case was sent to a magistrate judge who issued a report and recommendation to deny the petition. The report was issued one day after the Supreme Court issued its decision in Crawford holding that out-of-court statements by witnesses that are testimonial are barred under the Confrontation Clause. 541 U.S. at 59, 124 S.Ct. 1354. Consequently, Lave filed objections to the report and recommendation, arguing for the first time that Officer Hughes’ testimony violated his Sixth Amendment rights under the Confrontation Clause. He also argued that Crawford supported his ineffective assistance of counsel claims and filed a motion to “have federal proceedings held in abeyance pending exhaustion of new issues in state court.” The district court rejected his objections and his motion, finding that 1) Crawford did not apply retroactively; and 2) his counsel did not give ineffective assistance because he did not have the benefit of the Crawford decision at the time he conceded to allow Officer Hughes to testify. As a result, the district court adopted the magistrate’s report and recommendation and denied Lave’s petition. The district court subsequently denied Lave’s motion for a COA for essentially the same reasons.
[378]*378II
In order to appeal the district court’s denial of a habeas petition, Lave is required to first move for a COA. 28 U.S.C. § 2253(c)(1); Miller-El v. Cockrell, 537 U.S. 322, 336, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003) (explaining that a COA is a “jurisdictional prerequisite” without which “federal courts of appeals lack jurisdiction to rule on the merits of appeals from habeas petitioners”). To obtain a COA, Lave must make a “substantial showing of the denial of a constitutional right.” 28 U.S.C. § 2253(c)(2). That showing is made when a petition demonstrates that “reasonable jurists would find the district court’s assessment of the constitutional claims debatable or wrong.” Slack v. McDaniel, 529 U.S. 473, 484, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000). In other words, “[t]he question is the debatability of the underlying constitutional claim, not the resolution of that debate.” Miller-El, 537 U.S. at 342, 123 S.Ct. 1029.
A
Lave argues that his Sixth Amendment rights were violated when Officer Hughes testified as to what Bates had told him regarding Lave’s participation in the crime. The Confrontation Clause of the Sixth Amendment states that “[i]n all criminal prosecutions, the accused shall enjoy the right ... to be confronted with the witnesses against him.” U.S. Const, amend. VI. Last year, the Supreme Court held that, under this clause, “[t]estimonial statements of witnesses absent from trial [can be] admitted only where the declarant is unavailable, and only where the defendant has had a prior opportunity to cross-examine.” Crawford, 541 U.S. at 59, 124 S.Ct. 1354. The Court further noted that “[statements taken by police officers in the course of interrogations are also testimonial under even a narrow standard.” Id. at 52, 124 S.Ct. 1354. In this case, the parties do not dispute that Bates was available to testify and Lave was never given an opportunity to cross-examine him. Thus, under Crawford, reasonable jurists would find debatable whether Lave’s Sixth Amendment rights were violated through Officer Hughes’ testimony. Indeed, the State concedes that the “application of Crawford would undoubtedly afford Lave a new trial.”
However, this court has not decided whether Crawford may be applied retroactively on collateral review. Under the framework established by the Supreme Court in Teague v. Lane, 489 U.S. 288, 109 S.Ct. 1060, 103 L.Ed.2d 334 (1989), a specific rule may be applied retroactivity following a three step process:
First, the court must determine when the defendant’s conviction became final. Second, it must ascertain the legal landscape as it then existed, and ask whether the Constitution, as interpreted by the precedent then existing, compels the rule. That is, the court must decide whether the rule is actually “new.” Finally, if the rule is new, the court must consider whether it falls within either of the two exceptions to nonretroactivity.
Beard v. Banks, 542 U.S. 406, 124 S.Ct. 2504, 2510, 159 L.Ed.2d 494 (2004) (citations and quotations omitted). Thus, a new rule will be applied retroactively only if 1) it “places certain kinds of primary, private individual conduct beyond the power of the criminal law-making authority to proscribe” Teague, 489 U.S. at 311, 109 S.Ct. 1060; or 2) it is “a watershed rule[ ] of criminal procedure implicating the fundamental fairness and accuracy of the criminal proceeding.” Beard, 124 S.Ct. at 2513.
Various courts throughout the country have addressed this issue with conflicting results. The Second, Sixth, Seventh and Tenth circuits have all con-[379]*379eluded that while Crawford is a new rule, it is “not a watershed decision and is, therefore, not retroactively applicable to [a petitioner’s] initial habeas petition.” Brown v. Uphoff, 381 F.3d 1219, 1227 (10th Cir.2004); see also Mungo v. Duncan, 393 F.3d 327, 336 (2d Cir.2004) (“Because Teague’s test of a watershed rule requires improvement in the accuracy of the trial process overall, we conclude that Crawford is not a watershed rule ... [and] should not be applied retroactively on collateral review.”); Dorchy v. Jones, 398 F.3d 783, 788 (6th Cir.2005); and Murillo v. Frank, 402 F.3d 786, 789-91 (7th Cir.2005). In contrast, the Ninth Circuit recently rejected this approach and found that Crawford was retroactive because “the Crawford rule is one without which the likelihood of accurate conviction is seriously diminished.” Bockting v. Bayer, 399 F.3d 1010, 1021 (9th Cir.2005). Finally, several federal district and state courts have held that Crawford does not recognize a new constitutional rule because the “Court relied on the common law understanding of the hearsay rule and the prior interpretations of the Sixth Amendment to the United States Constitution.” Brown v. Dretke, No. Civ.A.SA-04CA-0543-X, Civ.A.SA-04CA-0725-X, 2004 WL 2538474, at *2 (W.D.Tex. Nov.8, 2004). See also Bunton v. Texas, 136 S.W.3d 355, 368-69 (Tex.App.2004). Compheating this issue, is Lave and his counsel’s stipulation to admit Officer Hughes’ testimony for tactical reasons. Indeed, in his prior murder trial, Lave objected to the admissibility of the same evidence for the exact reasons that under-gird Crawford. That objection, however, was overruled by the court. Nevertheless, given the Ninth Circuit’s decision in Bockt-ing, reasonable jurists would debate whether Crawford applies retroactively to Lave’s habeas petition. As a result, we grant the petitioner’s request for a COA on this issue.
B
In a related claim, Lave alleges that the district court erred in denying his ineffective assistance of counsel (“IAC”) claim based on his attorney’s decision to allow the prosecution to present Bates’ statement through Officer Hughes. In order to establish an IAC claim, Lave must demonstrate that 1) his counsel’s performance was deficient and 2) he was prejudiced by that deficient performance. Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). “The failure to .prove either deficient performance or actual prejudice forecloses an ineffective assistance of counsel claim.” Green v. Johnson, 160 F.3d 1029, 1035 (5th Cir.1998) (citing Moody v. Johnson, 139 F.3d 477, 483 (5th Cir.1998)). To demonstrate deficient performance, Lave must show that his counsel’s representation “fell below an objective standard of reasonableness.” Strickland, 466 U.S. at 688, 104 S.Ct. 2052. As to the second prong of the IAC test, to establish prejudice a “defendant must show that there is a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different. A reasonable probability is a probability sufficient to undermine confidence in the outcome.” Id. at 694,104 S.Ct. 2052.
Lave asserts that his trial counsel's decision to allow Bates' testimony through Officer Hughes was "irrational." In support, he cites to the Supreme Court's decision in Crawford and argues that "[w]ith Crawford-applied e.g. as an `old rule' not clearly recognized but binding at the time of Lave's trial-this is all the more obvious." However, the deficiency prong of an lAG claim "is judged by counsel's conduct under the law existing at the time of the conduct." Westley v. Johnson, 83 F.3d 714, 723, (5th Cir.1996) (emphasis added). Since Crawford was decid[380]*380ed years after Lave’s conviction, it cannot be the basis for his IAC claim.
Lave argues that the district court erred by concluding that since Lave expressly endorsed his counsel’s decision to allow Officer Hughes’ testimony regarding Bates’ statement, he is precluded from attacking that strategy. In support, the district court cited to United States v. Weaver, where the Seventh Circuit held that “[w]here a defendant, fully informed of the reasonable options before him, agrees to follow a particular strategy at trial, that strategy cannot later form the basis of a claim of ineffective assistance of counsel.” 882 F.2d 1128, 1140 (7th Cir.1989). However, the district court did not deny Lave’s IAC claim solely on the basis of his voluntary agreement. Rather, it also found that Lave’s counsel’s decision was not ineffective because it was part of a sound trial strategy. “A conscious and informed decision on trial tactics and strategy cannot be the basis for constitutionally ineffective assistance of counsel unless it is so ill chosen that it permeates the entire trial with obvious unfairness.” United States v. Jones, 287 F.3d 325, 331 (5th Cir.2002).
The State concedes that the district court erred when it stated that Lave’s counsel entered into this agreement because the defendant did not want Bates in front of the jury. According to the affidavit submitted by Lave’s trial counsel to the state habeas court, the decision to allow Officer Hughes to testify was precipitated by two developments. First, during his earlier trial for the murder of Banzhaf, Lave’s counsel did object to Officer Hughes’ testimony regarding Bates’ statements. That objection, however, was overruled by the court. Second, as Lave’s counsel noted in its affidavit:
We also agreed to have Officer Hughes testify because the State told us that they would most likely not call Bates as a witness (Because we could not offer and enforce immunity, we could not call Bates and override a Fifth Amendment assertion). We needed the jury to know about Bates’s statements because one of the State’s witnesses, Chris Gibbons, had left the impression that Lave killed the two boys, and Bates’ statements dispelled this impression. Thus we had no choice but to have Officer Hughes testify-
Lave acknowledges that while this was in fact his trial counsel’s strategy, it was still “erroneous[ ] in light of the law and what [his counsel] knew of the facts at the time.” No further explanation is given as to why he considers this strategy “erroneous.” Lave has failed to assert that his counsel’s decision was not “conscious and informed” or that “it [was] so ill chosen that it permeate[d] the entire trial with obvious unfairness.” Jones, 287 F.3d at 331. Lave’s silence in this matter leaves us to conclude that reasonable jurists would not find the district court’s decision to deny his IAC claim debatable or wrong. Thus, we deny Lave’s request for a COA on this issue.
C
Lave also contends that the district court abused its discretion by denying his request for limited discovery, including deposing Bates and DNA testing. He believes that this additional discovery is necessary to establish his claims of actual innocence, IAC, and the State’s alleged suppression of exculpatory evidence.
A habeas petitioner may “invoke the processes of discovery available under the Federal Rules of Civil Procedure if, and to the extent that, the judge in the exercise of his discretion and for good cause shown grants leave to do so, but not otherwise.” Rector v. Johnson, 120 F.3d 551, 562 (5th Cir.1997) (citing Perillo v. Johnson, 79 F.3d 441, 444 (5th Cir.1996)). [381]*381In order to establish good cause, the petitioner must demonstrate that “a factual dispute, if resolved in the petitioner’s favor, would entitle him to relief and the state has not afforded the petitioner a full and fair evidentiary hearing.” Ward v. Whitley, 21 F.3d 1355, 1367 (5th Cir.1994). Conclusional allegations are insufficient to warrant discovery; the petitioner must set forth “specific allegations of fact.” United States v. Webster, 392 F.3d 787, 802 (5th Cir.2004).
Lave argues that the district court’s refusal to allow him to depose Bates constitutes error because he was convicted based on statements made by Bates to the police officer. However, Lave has failed to assert that there is any factual dispute as to whether Bates actually stated that Lave had committed murder. Instead, he contends that the deposition is necessary to determine whether the State violated the “Confrontation Clause’s ‘truth-finding function.’ ” This determination is not contingent on the resolution of specific factual allegations because there is no dispute that the State sought to enter Bates’ testimony without the benefit of cross-examination. See Lee v. Illinois, 476 U.S. 530, 541, 106 S.Ct. 2056, 90 L.Ed.2d 514 (1986) (the “truthfinding function of the Confrontation Clause is uniquely threatened when an accomplice’s confession is sought to be introduced against a criminal defendant without the benefit of cross-examination”). Thus, since Lave has failed to show how Bates’ deposition would resolve a live factual dispute, reasonable jurists would not argue that the district court abused its discretion.
Similarly, Lave argues that DNA testing of blood evidence is necessary in order to challenge Bates’ statements. However, Lave has not indicated what specific information he anticipates DNA testing would provide and, more importantly, how that information could be used to impeach Bates’. credibility. In other words, Lave has once again failed to show how the additional discovery would resolve a specific factual dispute. Since this court does not “sanction fishing expeditions based on a petitioner’s conclusory allegations”, Lave’s motion for a COA on this matter is denied. Rector, 120 F.3d at 562.
D
Lave contends that his Fifth Amendment rights under the Double Jeopardy Clause were violated because, at the time of the trial, he had already been convicted of murdering Banzhaf, another victim from the same robbery that resulted in Marq-uart’s death. He argues that the prosecution’s decision not to seek the death penalty in the Banzhaf case constituted “a tacit admission of lack of confidence that there was sufficient evidence for the jury to find Lave death eligible as a party to capital murder under Texas law.” As a result, Lave alleges the prosecution was estopped from seeking the death penalty in this ease.
Lave’s argument is without merit. The Double Jeopardy Clause of the Fifth Amendment states that “[n]o person shall ... be subject for the same offence to be twice put in jeopardy of life or limb.” U.S. CoNst. amend. V. This Clause, however, applies only to capital-sentencing proceedings where such proceedings “have the hallmarks of the trial on guilt or innocence.” Sattazahn v. Pennsylvania, 537 U.S. 101, 106, 123 S.Ct. 732, 154 L.Ed.2d 588 (2003). As the Supreme Court noted, “an ‘acquittal’ at a trial-like sentencing phase, rather than the mere imposition of a life sentence, is required to give rise to double-jeopardy protections.” Id. at 107, 123 S.Ct. 732. Lave has not shown that reasonable jurists would debate whether the prosecution’s decision not to seek the death penalty is the equivalent of an “ac[382]*382quittal at a trial-like sentencing phase.” Moreover, double jeopardy only prohibits the State from “punishing twice, or attempting a second time to punish criminally for the same offense.” Witte v. United States, 515 U.S. 389, 396, 115 S.Ct. 2199, 132 L.Ed.2d 351 (1995) (emphasis added). Even though the death of Banzhaf and Marquart stemmed from the same robbery, these murders constitute separate offences. See Miller v. Turner, 658 F.2d 348, 350 (5th Cir.1981) (rejecting as “frivolous” defendant’s argument that “because the two murders for which he was charged occurred during the same criminal episode, his conviction and sentencing on two counts of murder violated the Double Jeopardy Clause of the Fifth Amendment.”). Accordingly, Lave’s motion for COA based on a double jeopardy claim is denied.
E
Finally, Lave argues that the district court abused its discretion by denying his motion to 1) hold the federal proceedings in abeyance to allow Lave to return to state court in order to exhaust his Crawford claim or 2) allow him to amend his federal habeas petition to include his Cratoford claim. Since a COA is not a prerequisite to review the denial of a motion to stay proceedings, we may at this stage address the merits of Lave’s contention. Dunn v. Cockrell, 302 F.3d 491, 492 (5th Cir.2002) (holding that a COA is only required when the petitioner is appealing “from the merits of his habeas petition”).
Under the Anti-Terrorism and Effective Death Penalty Act (AEDPA), a petitioner has one year from the date the Supreme Court announces a new retroactive constitutional rule to challenge his conviction based on this new rule. 28 U.S.C. § 2244(d)(1)(C). Recently, the Texas Court of Criminal Appeals announced that it would consider a successive state habeas petition if any concurrent federal proceedings are stayed pending completion of state proceedings. Ex parte Soffar, 143 S.W.3d 804 (Tex.Crim.App. 2004). The court reasoned that the change was necessary in order to address “[t]he problematic situation [] when the Supreme Court announces a ‘watershed’ procedural or substantive change in the law which applies retroactively to all cases, even those on collateral review.” Id. at 806. Accordingly, Lave’s contention turns on whether Crawford announces a retroactive “watershed procedural or substantive change in the law.” Since we have already granted a COA on this issue, we abstain from addressing this matter until after this court has resolved whether Crawford has created a new watershed rule that applies retroactively to Lave’s conviction.
Ill
For the forgoing reasons, Lave’s motion for a COA as to whether his Sixth Amendment rights were violated under the Confrontation Clause is granted. His petition for a COA on all other issues is denied. We abstain from ruling on whether the district court abused its discretion by not allowing Lave to amend his federal habeas petition or to return to state court, until we have addressed the retroactivity of Crawford.