
563 F.3d 766 (2009)
Johnny A. RUCKER, Jr., Appellant,
v.
Larry NORRIS, Director, Arkansas Department of Correction, Appellee.
No. 08-1970.
United States Court of Appeals, Eighth Circuit.
Submitted: December 10, 2008.
Filed: April 30, 2009.
*767 John Wesley Hall, Jr., argued, Little Rock, AR, for appellant.
Pamela Rumpz, AAG, argued, Little Rock, AR, for appellee.
Before LOKEN, Chief Judge, BEAM and ARNOLD, Circuit Judges.
LOKEN, Chief Judge.
An Arkansas jury convicted Johnny Rucker of capital murder. The Supreme Court of Arkansas affirmed the conviction and life sentence. Rucker v. State, 320 Ark. 643, 899 S.W.2d 447 (1995). The *768 state trial court denied Rucker's petition for postconviction relief; the Supreme Court of Arkansas again affirmed. In 2001, Rucker petitioned the state courts for postconviction relief under a new statute authorizing relief if "[s]cientific evidence not available at trial establishes the petitioner's actual innocence." Ark.Code Ann. § 16-112-201(a)(1) (2004). The trial court denied the petition after a limited hearing, and the Supreme Court of Arkansas affirmed.
Rucker then filed this federal habeas petition, asserting numerous claims. The district court[1] denied the petition but granted a certificate of appealability on two claims relating to the voluntariness of Rucker's confession and the denial of relief under the new-scientific-evidence statute. Reviewing the district court's denial of those claims de novo under the deferential standard of review mandated by the Anti-Terrorism and Effective Death Penalty Act of 1996 (AEDPA), we affirm. See 28 U.S.C. § 2254(d); Mark v. Ault, 498 F.3d 775, 782 (8th Cir.2007).

I. The Confession Claims
At the time of Cindi Smith's murder, Rucker, a crack cocaine addict, lived with Smith in her motor home in Arkadelphia, Arkansas. Smith's father found her body in the home, shot in the back of the head. A .22 caliber pistol was resting on her left hand. Her car was missing, and police learned that morning that someone was attempting to cash checks on her bank account. Rucker was arrested driving Smith's car. Her purse, blank checks, and.22 caliber shells were found in the car. Rucker admitted cashing checks and using the money to buy drugs. At the police station, he confessed that, while high on crack cocaine, he shot Smith because he did not want her to stop him from taking her car to obtain more drugs. Rucker dictated his statement to a police officer. A videotape recorded the officer reading the statement to Rucker, and Rucker reaffirming it.
Before trial, the trial court found after a hearing that Rucker's confession was voluntary and therefore admissible, a procedure mandated by Jackson v. Denno, 378 U.S. 368, 84 S.Ct. 1774, 12 L.Ed.2d 908 (1964). At trial, the court admitted evidence tending to discredit the confession by establishing that Rucker was under the influence of crack cocaine when he confessed the videotape, which showed Rucker's behavior when he reaffirmed the confession; testimony by a clinical psychologist that this behavior appeared to be influenced by cocaine use; testimony by the officer who recorded and read Rucker's confession that Rucker exhibited symptoms of drug intoxication; and testimony by other witnesses that Rucker had smoked crack on the day of the murder. However, the court excluded testimony by two inmates who had testified at the pretrial voluntariness hearing that Rucker appeared to be under the influence of drugs at the county jail a short time after he confessed.
At the end of the trial, defense counsel requested the following jury instruction:
A confession made by Johnny A. Rucker in the presence of police officers is presumed to be involuntary, and the burden is on the state to overcome that presumption by a preponderance of the evidence.
The court denied the request because it had previously found the confession voluntary. During closing argument, defense counsel argued at length that, for various *769 reasons, including the fact that Rucker was high on drugs, his confession should not be credited.
On direct appeal, Rucker argued that the trial court erred in excluding testimony by the two inmates. The Supreme Court of Arkansas acknowledged prior decisions recognizing a defendant's constitutional right to have the jury consider "the weight and credibility" of a voluntary confession. The Court nonetheless affirmed on the ground that the proffered testimony would have been cumulative to other evidence that Rucker was high on drugs before and after the crime, and therefore "even if the exclusion of the testimony was error, it was harmless error in this instance." 899 S.W.2d at 450.
In his first state postconviction proceeding, Rucker argued that trial counsel's failure to request a proper jury instruction one that related to the confession's credibility, rather than to its voluntariness was ineffective assistance of counsel under Strickland v. Washington, 466 U.S. 668, 694-95, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). The Supreme Court of Arkansas rejected that contention, reasoning that any alternative instruction would have been rejected because, under Arkansas law, the issue of voluntariness is for the court, not the jury, and once the court determines the confession is admissible, "it will be a matter of argument of counsel as to the weight to be given that evidence." Though within the scope of the certificate of appealability granted by the district court, Rucker does not argue this issue on appeal.
On appeal, Rucker first argues that the Supreme Court of Arkansas erred in rejecting his postconviction jury instruction argument because the Sixth Amendment right to present a complete defense includes the right to have the credibility of a confession determined by the jury, and the jury must be properly instructed on this issue. He relies primarily on Crane v. Kentucky, 476 U.S. 683, 690-91, 106 S.Ct. 2142, 90 L.Ed.2d 636 (1986), which held that the "wholesale exclusion" of evidence pertaining to the credibility of a confession violates a defendant's constitutional right to a meaningful opportunity to present a complete defense. As the district court correctly concluded, this issue is procedurally barred because it was not "fairly present[ed]" to the appropriate state court. Baldwin v. Reese, 541 U.S. 27, 29, 124 S.Ct. 1347, 158 L.Ed.2d 64 (2004); see 28 U.S.C. § 2254(b)(1).
On direct appeal, Rucker argued only the witness exclusion issue. On appeal from the denial of postconviction relief, he cited Crane and a prior Arkansas decision to the same effect, Kagebein v. State, 254 Ark. 904, 496 S.W.2d 435, 440 (1973). But he argued only ineffective assistance of counsel under Strickland, not that the trial court committed federal constitutional error in not instructing the jury that it must determine the credibility of his confession. A constitutional claim of ineffective assistance of counsel does not preserve a federal constitutional challenge "to the underlying legal rules that the allegedly ineffective counsel should have invoked." Ford v. Norris, 364 F.3d 916, 918 (8th Cir.2004).
We also agree with the district court that this jury instruction claim is without merit, even if not procedurally barred. Under Arkansas law, voluntariness is decided by the court, not the jury. Ark.Code Ann. § 16-89-107(b)(1). This is constitutionally permissible. See Jackson, 378 U.S. at 391 n. 19, 84 S.Ct. 1774; Lego v. Twomey, 404 U.S. 477, 484 & n. 9, 92 S.Ct. 619, 30 L.Ed.2d 618 (1972). At Rucker's trial, the court admitted evidence addressing the credibility of his confession, and defense counsel vigorously pressed the issue in closing argument. Neither Crane *770 nor any other Supreme Court decision has "clearly established" that the defendant has a constitutional right to a jury instruction on this credibility issue. 28 U.S.C. § 2254(d)(1).
Rucker next argues that the trial court violated his constitutional right to present a complete defense when it excluded testimony by two inmates supporting the argument that his confession was not credible because he was under the influence of crack cocaine. Rucker raised this evidentiary issue in his direct appeal to the Supreme Court of Arkansas. Though his appeal brief cited only Arkansas authorities, it relied on Leach v. State, 38 Ark. App. 117, 831 S.W.2d 615 (1992), and Kagebein, 496 S.W.2d 435, in arguing that "a defendant may present evidence at trial relevant to the weight and credibility of the confession." The opinion in Leach, 831 S.W.2d at 621, quoted at length from Crane in reversing the grant of the State's motion to preclude evidence addressing the credibility of a confession. Kagebein, 496 S.W.2d at 440, held that a defendant has a constitutional right to present evidence challenging the weight and credibility of a voluntary confession, relying in part on the Supreme Court's decision in Lego, 404 U.S. 477, 92 S.Ct. 619, which the Court followed in Crane. In affirming Rucker's conviction, the Supreme Court of Arkansas, citing Kagebein, acknowledged this constitutional right but held that any trial court error was harmless. 899 S.W.2d at 450. In these circumstances, this federal constitutional claim based upon Crane is not procedurally barred.
However, the district court correctly denied Rucker relief on the merits of this claim. Crane proscribed only the "wholesale exclusion" of evidence pertaining to the credibility of a confession. 476 U.S. at 691, 106 S.Ct. 2142. The Court carefully explained that it was not questioning "the power of States to exclude evidence through the application of evidentiary rules that themselves serve the interests of fairness and reliability," nor the "wide latitude" given trial judges to exclude "repetitive" evidence, "marginally relevant" evidence, and evidence posing an undue risk of harassment, prejudice, or confusion of the issues. Id. at 689-90, 106 S.Ct. 2142 (quotations omitted). In this case, the trial court admitted substantial evidence that Rucker was high on drugs before and after the crime, and defense counsel argued the credibility issue at length in closing argument. The Supreme Court of Arkansas concluded that the excluded evidence was cumulative and in any event that its exclusion was harmless error. 899 S.W.2d at 450. This decision was neither contrary to nor an unreasonable application of Rucker's constitutional right as construed in Crane to present evidence bearing on the credibility of his confession. 28 U.S.C. § 2254(d)(1); see Greer v. Minnesota, 493 F.3d 952, 959-60 (8th Cir.) (Crane error harmless), cert. denied, ___ U.S. ___, 128 S.Ct. 672, 169 L.Ed.2d 527 (2007); United States v. Martin, 369 F.3d 1046, 1059 (8th Cir.) (same), cert. denied, 543 U.S. 1035, 125 S.Ct. 817, 160 L.Ed.2d 599 (2004).

II. The New Scientific Evidence Claim
Rucker argues that the state courts violated his federal constitutional rights to due process and to present a complete defense by denying his postconviction petition to require additional fingerprint testing of the gun found near Smith's body pursuant to the new state habeas cause of action enacted by the Arkansas Legislature in 2001. The firearm was tested for fingerprints during the initial murder investigation, but no identifiable prints were found. In the state courts, Rucker argued that additional tests should be performed using the latest technology, and that any prints found should be compared to those *771 of four persons Rucker alleged might have committed the murder, and to a new state database containing some 600,000 sets of fingerprints. After an evidentiary hearing at which the chief latent prints examiner of the Arkansas State Crime Laboratory testified that no new technology "would produce an identifiable print," the state courts denied relief on the ground that Rucker failed to show that the requested testing "has the scientific potential to produce new noncumulative evidence materially relevant to the defendant's assertion of actual innocence." Ark.Code Ann. § 16-112-202(c)(1)(B) (2004).[2]
This habeas claim is procedurally barred because Rucker raised no issue of federal constitutional law and cited no federal authority in the state courts. See Carney v. Fabian, 487 F.3d 1094, 1096 (8th Cir.) (federal due process violation must be specifically asserted in state court), cert. denied, ___ U.S. ___, 128 S.Ct. 721, 169 L.Ed.2d 564 (2007). Whether the state courts misinterpreted or misapplied the Arkansas statute authorizing state habeas relief based upon new scientific evidence is not a basis for federal habeas corpus relief. Evenstad v. Carlson, 470 F.3d 777, 782 (8th Cir.2006).
Moreover, even if the federal claim had been raised in state court, Rucker cites no Supreme Court decision clearly establishing that the right to present a complete defense applies to postconviction proceedings, or that due process includes the right to postconviction testing using new technological advances. We did not resolve that due process issue in Tyler v. Purkett, 413 F.3d 696 (8th Cir.2005). Nor have our sister circuits resolved it. See McKithen v. Brown, 481 F.3d 89, 106-08 (2d Cir. 2007); Grayson v. King, 460 F.3d 1328, 1336-43 (11th Cir.2006); Harvey v. Horan, 278 F.3d 370, 378-79 (4th Cir.2002), all actions brought under 42 U.S.C. § 1983.
Rucker further argues that the district court abused its discretion by not ordering the fingerprint testing he requested under Rule 6(a) of the Rules Governing Section 2254 Cases in the United States District Courts. We disagree. The "good cause" that authorizes discovery under Rule 6(a) requires a showing "that the petitioner may, if the facts are fully developed, be able to demonstrate that he is ... entitled to [habeas] relief." Bracy v. Gramley, 520 U.S. 899, 909, 117 S.Ct. 1793, 138 L.Ed.2d 97 (1997) (quotation omitted). As Rucker's federal claim is procedurally barred because it was not raised in the state courts, he cannot satisfy this requirement. Moreover, the state courts' decision that Rucker failed to show "more than a slight chance" that additional testing would yield a favorable result was not "based on an unreasonable determination of the facts." 28 U.S.C. § 2254(d)(2).
The judgment of the district court is affirmed.
NOTES
[1]  The HONORABLE JERRY W. CAVANEAU, United States Magistrate Judge for the Eastern District of Arkansas, who exercised jurisdiction over the case with the consent of the parties. See 28 U.S.C. § 636(c).
[2]  This section was rewritten in 2005. See § 16-112-202(8) (2006). The state courts applied the version in effect when Rucker filed his petition.
