JACOBS, Circuit Judge.

Robie J. Drake appeals from a judgment of the United States District Court for the Western District of New York (Elfvin, J.) denying a writ of habeas corpus pursuant to 28 U.S.C. § 2254. In 1982, Drake was convicted by a jury in New York State Supreme Court, Niagara County, on two counts of second degree murder for the shooting of a young couple in a parked car in an isolated area near a junkyard. The defense theory was that Drake often used abandoned cars for target practice, that he shot up the victims’ car without realizing it was occupied, and afterward in panic stabbed the young man (who was dying), and drove the car to a nearby dump. To aid the prosecution of a crime that was seemingly without motive, the prosecutor at the last minute called to the witness stand a putative expert who testified about a syndrome of sexual dysfunction that appeared to account for the particular, gruesome circumstances of the crime. Farfetched as the defense theory was, the prosecution concedes that the expert was recruited late in the trial to plug a perceived hole in its case concerning intent. It is now clear that the expert’s qualifications were largely perjured, and that the syndrome, dubbed “picquerism,” is referenced nowhere but in a true-crime paperback. The prosecution successfully opposed a continuance sought by Drake’s counsel, who protested that he had been unable to find a psychologist who had even heard of “picquerism.”

Drake claims on habeas that (i) his right to due process under the Fourteenth Amendment and his Sixth Amendment right to compulsory process were violated because the surprise testimony, coupled with the denial of a continuance, deprived him of the opportunity to present a meaningful defense; and (ii) his due process rights under the Fourteenth Amendment were violated because the prosecution knew or should have known of the perjury.

*341 BACKGROUND

On the night of December 5-6, 1981, teenagers Amy Smith and Stephen Rosen-thal were in Rosenthal’s rusty 1969 Chevy Nova in the parking lot of a factory in the Town of North Townawanda, New York. The factory parking lot was adjacent to a junkyard with abandoned vehicles. The teenagers were using the spot as a lovers’ lane. It is undisputed that Drake shot them to death shortly after midnight.

In a confession, Drake said that he left home at approximately 11:30 p.m., dressed in military fatigues and armed with a loaded Marlin .22 caliber semi-automatic rifle, a loaded Winchester .22 caliber high powered rifle, extra ammunition and two hunting knives, and that he went to the junkyard looking for abandoned vehicles to use in target practice. He said that the first vehicle he came across was the parked Nova, that he believed the car to be abandoned because the engine was off and no noise came from within, and that he opened fire on the passenger side window of the car with his semi-automatic rifle.

Drake claimed that he did not intend to kill Smith and Rosenthal, and insisted that he learned of their deaths only when he inspected the car, heard Rosenthal groaning, and opened the door to find the two bodies. According to Drake, he stabbed Rosenthal twice, in a fit of panic, to stop him from groaning, but that he “didn’t mean to kill him or anything.” Trial Transcript at 267. According to Drake, Rosen-thal was fully clothed, Smith not. Unsure of what to do, he drove the Nova car to a secluded spot down the road from the parking lot, and put Rosenthal’s body in the trunk. Surprised by a passing car, Drake got back in the car and drove to the Niagara County dump in the neighboring town of Wheatfield, where he was putting Smith’s body into the trunk when he was spotted by two police officers on routine patrol.

The only issue at trial was whether Drake had the intent requisite for second degree murder. The prosecution’s case was supported by a good deal of circumstantial evidence. Drake stated in his confession that he could not see into the car because the windows were fogged up, an indication that the car may have been occupied. Drake’s semi-automatic rifle could fire nineteen rounds of ammunition in a single clip, and Drake fired them all. The autopsies showed that Smith died from two gunshot wounds to the head, and that Ro-senthal died from fourteen gunshot wounds to his face, neck and chest. (The stab wounds were not the cause of Rosen-thal’s death.) A student at the high school attended by Drake and the victims testified that, a few weeks prior to the shooting, Drake and Rosenthal argued while passing each other in the hallway.

Physical evidence supported the prosecution’s theory that this was a sex-crime. The emergency room physician who pronounced the victims dead testified concerning sexual trauma to Smith, including a bruised rectum, and mud near her private parts. The medical examiner who performed the autopsies noted a bite-mark on Smith’s left breast, with hemorrhaging so minor as to indicate that the bite had been inflicted post-mortem. The prosecution’s medical forensic witness found no evidence of semen anywhere except on Drake’s underwear. Forensic experts who performed a second autopsy following the exhumation of Smith’s body a month after her death, confirmed that the bite on Smith’s right breast was inflicted postmortem, and also found a post-mortem bite mark on the other breast. Dr. Lowell Levine, a dentist and forensic odontologist with experience in bite marks, confirmed the presence of the two post-mortem *342 marks on each breast. Over a defense objection, Dr. Levine opined that bite marks are often present in “sexually [sic] or demented type[s] of crimes.” Trial Transcript at 671.

Justice Aldo L. DiFlorio had advised the parties pretrial that because of an out-of-town judicial commitment, the trial would have to conclude no later than Tuesday of the week following its commencement. The prosecution informed defense counsel on the Thursday evening that it intended to call a psychologist named Richard D. Walter to testify about psychological profiling. On the Friday, the prosecution successfully moved to add Walter as a witness, and Walter mounted the stand. Under the announced schedule, defense counsel would have no more than a weekend to get a competing expert, if needed, or for that matter to prepare his cross-examination.

The prosecution concedes that Walter’s testimony was intended to reinforce what it perceived as weaknesses in the evidence supporting its theory of intent. The prosecution also concedes that Walter was referred to them by Dr. Levine, the forensic dentist, and that the prosecution did not independently investigate Walter’s qualifications.

Walter conceded at the outset that he had not examined Drake or reviewed his medical records, and would rely on his review of grand jury testimony, medical evidence and the police record. Walter opined on that basis that Smith and Ro-senthal had been the victims of a specific type of “lust-murder” called “picquerism” (a derivative misspelling of the French verb “piquer,” which means, among other things, to stick or poke). See Trial Transcript at 794. According to Walter, pic-querists achieve sexual gratification by biting, shooting, stabbing, and sodomizing their victims (though not all picquerists do all these things). This supposed syndrome accounted for much of the physical evidence in medical terms that dovetailed with the prosecution’s theory of intent.

It is now apparent that Walter’s testimony concerning his qualifications was perju-rious. He claimed extensive experience in the field of psychological profiling, including: work on 5000 to 7500 cases over several years in the Los Angeles County Medical Examiner’s Office; an adjunct professorship at Northern Michigan University; more than four years as a prison psychologist with the Michigan Department of Corrections; and expert testimony given at hundreds of criminal trials in Los Angeles and Michigan.

On the Monday following Walter’s testimony, defense counsel told Justice DiFlo-rio that the defense had searched over the weekend to retain a rebuttal psychologist, but could not find any expert who had ever heard of “picquerism.” The defense requested a two-week continuance to find a psychologist with the expertise required. The prosecution successfully opposed a continuance.

The trial concluded on schedule. Drake was convicted and sentenced to two consecutive terms of twenty years to life. The Appellate Division, Fourth Department, affirmed the conviction, and the Court of Appeals denied leave to appeal. Drake’s petition for a writ of error coram nobis, arguing ineffective assistance of appellate counsel, was denied by the Appellate Division.

Years after exhausting his direct appeals, Drake discovered evidence, through his own research in prison, that Walter had lied about his credentials. Although Walter is a prison psychologist with the Michigan Department of Corrections, = Drake found suggestive evidence that Walter lied about his other credentials. As *343 the prosecution now concedes, Walter performed no criminal profiling in the Los Angeles County Medical Examiner’s Office. According to Walter’s supervisors there, he was employed as a lab assistant responsible for cleaning and maintaining the forensic lab. There seems to be no record that Walter was ever on the payroll of Northern Michigan University, where he claimed to be an adjunct professor. The Los Angeles County District Attorney’s office has found no record of Walter testifying as an expert witness in a criminal proceeding between October 1975 through May 1978. 1

In 1995, Drake moved to vacate his conviction and sentence pursuant to N.Y. C.P.L. § 440.10 on the basis of the newly discovered evidence concerning Walter’s perjury. The Supreme Court, Niagara County, denied the motion without a hearing. The Fourth Department affirmed that order. The Court of Appeals denied leave to appeal.

This habeas petition followed.

DISCUSSION

We review the district court’s denial of a habeas petition de novo. Fama v. Comm’r of Corr. Servs., 235 F.3d 804, 808 (2d Cir.2000).

Under the Antiterrorism and Effective Death Penalty Act of 1996 (“AED-PA”), a federal habeas court must apply a deferential standard of review to “any claim that was adjudicated on the merits in State court.” 28 U.S.C. § 2254(d). “[A] state court ‘adjudicate^]’ a state prisoner’s federal claim on the merits when it (1) disposes of the claim ‘on the merits,’ and (2) reduces its disposition to judgment.” Sellan v. Kuhlman, 261 F.3d 303, 312 (2d Cir .2001).

Drake raises two claims on appeal from the district court’s denial of his habe-as petition: (i) that his right to due process under the Fourteenth Amendment and his Sixth Amendment right to compulsory process were violated because the surprise testimony, coupled with the denial of a continuance, deprived Drake of the opportunity to present a meaningful defense; and (ii) that his due process rights under the Fourteenth Amendment were violated because the prosecution knew or should have known of the perjury. Each of these claims was adjudicated on the merits in state court. People v. Drake, 129 A.D.2d 963, 514 N.Y.S.2d 280, 282 (4th Dep’t 1987) (“The defendant had a full and fair opportunity to cross-examine the People’s expert and to present opposing views, and the trial court properly charged the jurors that they could accept or reject the expert testimony in whole or in part.”); People v. Drake, 256 A.D.2d 1159, 684 N.Y.S.2d 102, 102 (4th Dep’t 1998) (“While [evidence of Walter’s perjury] ‘might have affected the jury’s assessment of his credibility, there is nothing in the record indicating that the prosecution was aware, or should be charged with knowledge that he was misrepresenting his credentials.’ ” (citation omitted)). AEDPA’s deferential standard of review therefore applies.

Under that standard, no federal habeas relief is available unless the state court proceedings “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.” 28 *344 U.S.C. § 2254(d)(1). Drake contends that the state courts’ rejection of his state ha-beas petition amounted to an “unreasonable application” of clearly established Supreme Court precedent. “Under the ‘unreasonable application’ clause, a federal habeas court may grant the writ if the state court identifies the correct governing principle from [the Supreme] Court’s decisions but unreasonably applies that principle to the facts of the prisoner’s case.” Williams v. Taylor, 529 U.S. 362, 413, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000) (O’Connor, /., writing for the Court in Part II). Relief may not be granted on the ground that the habeas court “concludes in its independent judgment that the relevant state-court decision applied clearly established federal law erroneously or incorrectly. Rather, that application must also be unreasonable.” Id. at 411, 120 S.Ct. 1495.

With this standard in mind, we turn to Drake’s claims.

Drake argues that he was prevented from mounting a meaningful defense because the state trial court allowed Walter’s surprise testimony but denied Drake the continuance needed to counter it. “The rights to confront and cross-examine witnesses ... in one’s own behalf have long been recognized as essential to due process.” Chambers v. Mississippi, 410 U.S. 284, 294, 93 S.Ct. 1038, 35 L.Ed.2d 297 (1973); see also Washington v. Schriver, 255 F.3d 45, 56 (2d Cir.2001) (“The right to call witnesses in order to present a meaningful defense at a criminal trial is a fundamental constitutional right secured by both the Compulsory Process Clause of the Sixth Amendment and the Due Process Clause of the Fourteenth Amendment.”).

Here, however, the state court did not curtail cross-examination or exclude rebuttal by the defense. Drake’s disadvantage flowed from a refusal to grant a continuance, which is a matter “traditionally within the discretion of the trial judge.” Ungar v. Sarafite, 376 U.S. 575, 589, 84 S.Ct. 841, 11 L.Ed.2d 921 (1964); accord Morris v. Slappy, 461 U.S. 1, 11, 103 S.Ct. 1610, 75 L.Ed.2d 610 (1983). “[0]nly an unreasoning and arbitrary ‘insistence upon expeditiousness in the face of a justifiable request for delay’ violates the [Constitution].” Morris, 461 U.S. at 12, 103 S.Ct. 1610 (quoting Ungar, 376 U.S. at 589, 84 S.Ct. 841). The Appellate Division affirmed the trial court’s ruling, and we are constrained under AEDPA to assume that the Appellate Division’s decision was the product of considered judgment. See 28 U.S.C. § 2254(d).

Scheduling is a matter that is of necessity committed to the sound discretion of the trial court. The only motion for continuance presented to the trial court was Drake’s request for a two-week continuance in a jury trial. The Appellate Division presumably decided that the denial of that motion did not deprive Drake of his rights under the Sixth and Fourteenth Amendments. Drake identifies no Supreme Court authority that would command either the two-week continuance in a jury trial, or a new trial by reason of its denial. Of course, the state trial court could have provided a shorter continuance than the two weeks Drake sought; but it does not appear to be an unreasonable application of federal constitutional law to fail to provide a shorter continuance than requested. Under AEDPA, a reasonable application of Supreme Court precedent includes an application of law that we consider to be erroneous. See Williams, 529 U.S. at 411, 120 S.Ct. 1495.

The Supreme Court analyzes claims for wrongful conviction based on perjured tes *345 timony under the Due Process Clause of the Fourteenth Amendment. Napue v. Illinois, 360 U.S. 264, 269, 79 S.Ct. 1173, 3 L.Ed.2d 1217 (1959). Under this standard, the Court has said that the conviction must be set aside if (1) “the prosecution knew, or should have known, of the perjury,” 2 and (2) “there is any reasonable likelihood that the false testimony could have affected the judgment of the jury.” United States v. Agurs, 427 U.S. 97, 103, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976). Since Agurs was decided on the basis of actual knowledge (under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963)), the language providing for habeas relief where the prosecution “should have known” of the perjury is in the nature of dictum. We have not yet considered what it takes to show that the prosecution “should have known” it was sponsoring perjury or, among other things, whether this standard entails an exercise of due diligence. However, we decline to draw the contours of the phrase “should have known” unless we are presented with a case that requires us to do so. Here, we lack a sufficient factual record to decide whether the Appellate Division unreasonably applied federal law in concluding that the prosecutor neither knew nor should have known of Walter’s perjury.

In earlier proceedings, both the state habeas court and the Appellate Division, Fourth Department, found that Drake had made no showing that the prosecution knew or should have known about Walter’s perjury. Under AEDPA, a state court’s factual findings enjoy a presumption of correctness and may not be disturbed except upon a showing of “clear and convincing evidence.” 28 U.S.C. § 2254(e)(1). Here, however, the state court summarily denied without a hearing Drake’s § 440.10 motion to vacate, and thus there are no findings of fact requiring deference.

The Appellate Division offered only its bare conclusion that the record failed to establish “the prosecution was aware, or should be charged with knowledge that [Walter] was misrepresenting his credentials.” Drake, 684 N.Y.S.2d at 102 (internal quotation and citation omitted). Ordinarily, a state court’s conclusions of law are also entitled to considerable deference under AEDPA. See 28 U.S.C. § 2254(d). But because the state courts did not permit the development of the factual record, and because the Appellate Division relied on that incomplete record, there is at present no way for a federal habeas court to assess whether the Appellate Division’s conclusion represented an unreasonable application of federal law — i.e., whether the prosecution knew Walter’s testimony to be perjured, or “should have known” as much, whatever degree of complicity or negligence (or worse) that phrase may entail.

We conclude that Drake should be permitted to develop the record further. “ ‘[W]here 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 court to provide the necessary facilities and procedures for an adequate inquiry.’ ” Bracy v. Gramley, 520 U.S. 899, 908-09, 117 S.Ct. 1793, 138 L.Ed.2d 97 (1997) (ellipsis in original; quoting Harris v. Nelson, 394 *346 U.S. 286, 300, 89 S.Ct. 1082, 22 L.Ed.2d 281 (1969)). Although a “habeas petitioner, unlike the usual civil litigant in federal court is not entitled to discovery as a matter of ordinary course,” discovery may be granted upon a showing of “good cause.” Id. at 904, 117 S.Ct. 1793; Rules Governing § 2254 cases, Rule 6(a), 28 U.S.C. Foil. § 2254. We think that Drake has made a showing of good cause here, and that the record does provide a sufficient basis to remand this case to the district court for limited discovery on the circumstances surrounding Walter’s perjured testimony.

Drake points to the prosecution’s “covert and evasive” behavior as evidence of its knowing complicity in Walter’s perjured testimony. The prosecutor evidently made no independent inquiry into Walter’s background, and relied entirely on the recommendation of a dentist to vet the prosecution’s chief witness on aberrant psychology. The prosecutor had been advised that a scheduling constraint would require that the trial conclude no later than a Tuesday certain; the prosecution nevertheless presented Walter’s surprise testimony on the previous Friday, leaving no more than a weekend for the defense to investigate Walter’s qualifications and the esoteric psychological condition about which he testified. Although defense counsel protested that over the weekend he could find no psychologist who had so much as heard of picquerism, the prosecution opposed a continuance. The prosecution concedes that Walter’s highly prejudicial testimony was intended to bolster what it thought to be a significant weakness in its case on intent, the sole issue at trial.

If Drake can successfully establish that the prosecution knew or should have known of the perjured testimony, he may be able to establish a “reasonable likelihood that the false testimony could have affected the judgment of the jury.” Agurs, 427 U.S. at 103, 96 S.Ct. 2392. But see Drake, 684 N.Y.S.2d at 102 (finding “no reasonable probability that the verdict would have been different had the evidence [of perjury] been available to defendant and used by him to impeach the expert”). The state trial judge allowed expert testimony that the defendant in a murder trial was a sexual degenerate or some kind of ghoul, allowed that testimony so that the prosecution could rely upon it to bolster its case on intent (the only trial issue), and then denied the defendant a continuance to afford the defense an opportunity to confirm counsel’s grounded suspicion (later confirmed) that the witness was a charlatan, and that his testimony was, medically speaking, nonsense.

Moreover, the jury was likely to be impressed (if not inflamed) by testimony that the defendant was a “piequerist” who killed, mutilated, and abused his victims to satisfy a warped sexual urge. While Walter’s false statements went to his credentials, the Fourteenth Amendment “does not cease to apply merely because the false testimony goes only to the credibility of the witness.” Napue v. Illinois, 360 U.S. 264, 269, 79 S.Ct. 1173, 3 L.Ed.2d 1217 (1959). Here, the force of Walter’s substantive testimony came in large measure from his purportedly extensive experience in the field of criminal profiling.

The district court may decide to conduct an evidentiary hearing to determine whether the prosecution knew or should have known of the perjured testimony. If any witness is available who can testify to the events of the trial in 1982, an evidentiary hearing would certainly be indicated. A petitioner who “failed to develop the factual basis of a claim in State Court proceedings” is ordinarily barred *347 from seeking an evidentiary hearing in federal court. 28 U.S.C. § 2254(e)(2). However, “a petitioner cannot be said to have ‘failed to develop’ a factual basis for his claim unless the undeveloped record is a result of his own decision or omission.” McDonald v. Johnson, 139 F.3d 1056,1059 (5th Cir.1998). “[W]here, as here, a habe-as petitioner has diligently sought to develop the factual basis underlying his habeas petition, but a state court has prevented him from doing so, § 2254(e)(2) does not apply.” 3 Miller v. Champion, 161 F.3d 1249, 1253 (10th Cir.1998); see also Nieblas v. Smith, 204 F.3d 29, 31 (2d Cir.1999) (“A district court has broad discretion to hear further evidence in habeas cases” where § 2254(e)(2) does not preclude an evidentiary hearing).

If Drake can show that the prosecution knew (or should have known) about Walter’s perjured testimony, relief may be justified. On habeas review, courts apply a test for harmless error that looks to whether the error “ ‘had substantial and injurious effect or influence in determining the jury’s verdict.’ ” 4 Brecht v. Abrahamson, 507 U.S. 619, 638, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993) (quoting Kotteakos v. United States, 328 U.S. 750, 776, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946)). The state courts on collateral review did not reach the issue of harmless error because they ruled that there had been no constitutional error. Thus no state ruling on that issue commands deference under AEDPA. Moreover, under the Brecht standard, it seems likely that the perjured testimony would have had a substantial and injurious effect on the jury’s verdict, and thus that if the prosecution knew or should have known of the perjury, the constitutional error was not harmless.

CONCLUSION

For the foregoing reasons, we vacate the district court’s judgment denying Drake’s petition for habeas relief, and remand to the district court for discovery and a hearing (if the district court in its discretion considers that a hearing is needed) on whether the prosecution knew (or should have known) that its expert, Richard D. Walter, was committing perjury.

. The prosecution counters hopefully that Drake has provided no evidence as to whether Walter testified between 1978 and the time of trial in 1982; but it is hard to say whether giving expert testimony in other cases, without expert credentials, would rehabilitate him much.

. Drake argues that this Court’s decision in Sanders v. Sullivan, 863 F.2d 218 (2d Cir. 1988), permits the granting of habeas relief even in the absence of prosecutorial knowledge of perjury. However, in that case we explicitly relied on Justice Douglas' dissent in Durley v. Mayo, 351 U.S. 277, 290-91, 76 S.Ct. 806, 100 L.Ed. 1178 (1956). See Sanders, 863 F.2d at 223-24. AEDPA permits us to rely only on clearly established Supreme Court precedent.

. Oddly, the statute provides that a petitioner who "failed to develop the factual basis of a claim in State Court proceedings’’ is barred from seeking an evidentiary hearing in federal court unless (among other requirements) "the claim relies on ... a factual predicate that could not have been previously discovered through the exercise of due diligence." § 2254(e)(2)(A)(ii). Because Drake did not "fail” to do what he could in state court, we need not now consider in what circumstances a petitioner who "failed” to develop the record in state court can show nevertheless that he exercised due diligence.

. It appears to be an unsettled question in this Circuit whether, in light of the AEDPA regime, (i) we apply the Brecht harmless error standard directly or (ii) ask if the state court’s application of that standard was unreasonable. See Ryan v. Miller, 303 F.3d 231, 254 (2d Cir.2002).