
499 F.3d 752 (2007)
Winston BELL-BEY, Appellant,
v.
Donald ROPER, Appellee.
No. 06-2105.
United States Court of Appeals, Eighth Circuit.
Submitted: April 12, 2007.
Filed: August 17, 2007.
*753 *754 James W. Erwin, argued, St. Louis, MO (Thomas E. Douglass on the brief), for appellant.
Stephen D. Hawke, AAG, Jefferson City, MO, for appellee.
Before LOKEN, Chief Judge, BYE, and RILEY, Circuit Judges.
RILEY, Circuit Judge.
Winston Bell-Bey (Bell-Bey) appeals the district court's[1] denial of Bell-Bey's *755 application for a writ of habeas corpus pursuant to 28 U.S.C. § 2254. We affirm.
I. BACKGROUND
On June 3, 1994, Bell-Bey doused Fay Allen (Allen), his wife, with gasoline and lit Allen on fire. Allen suffered burns over 90% of her body and died two weeks later. Bell-Bey was convicted of first-degree murder and sentenced to death. The Supreme Court of Missouri reversed Bell-Bey's conviction and sentence and remanded for a new trial based upon the trial court's improper admission of hearsay evidence. State v. Bell (Bell-Bey I), 950 S.W.2d 482, 484-85 (Mo.1997) (en banc). On remand, Bell-Bey was convicted of first-degree murder and armed criminal action, and sentenced to concurrent terms of life imprisonment without parole. The Missouri Court of Appeals affirmed Bell-Bey's conviction and sentence. State v. Bell (Bell-Bey II), 14 S.W.3d 67 (Mo.Ct. App.1999) (per curiam). Bell-Bey filed a motion for post-conviction relief in state court. The state court held an evidentiary hearing and denied the motion. Bell-Bey also filed a motion to recall the mandate in Bell-Bey II. The Missouri Court of Appeals affirmed the denial of Bell-Bey's motion for post-conviction relief and denied the motion to recall the mandate. State v. Bell (Bell-Bey III), 83 S.W.3d 670, 677 (Mo.Ct.App.2002).
Bell-Bey filed an application for a writ of habeas corpus in federal district court, alleging five grounds for habeas relief: (1) the improper admission of hearsay evidence and the Missouri Court of Appeals's incorrect application of the harmless-error standard in reviewing the error; (2) the trial court erred by calling a witness a "lying witness" outside of the presence of the jury; (3) a Batson v. Kentucky, 476 U.S. 79, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986), challenge; (4) the improper exclusion of certain business records; and (5) the answering of a jury question without first consulting the attorneys. A magistrate judge issued a report and recommendation to deny habeas relief and to grant a certificate of appealability on the first ground for relief. The district court adopted the report and recommendation as modified, denied habeas relief, and granted a certificate of appealability on the first and fourth grounds for relief. This appeal followed. We additionally granted a certificate of appealability on the third ground for relief.
II. DISCUSSION
We review for clear error the district court's factual findings and review de novo its legal conclusions. Garcia v. Mathes, 474 F.3d 1014, 1017 (8th Cir.2007). The Antiterrorism and Effective Death Penalty Act of 1996 (AEDPA), Pub.L. No. 104-132, 110 Stat. 1214, limits the availability of habeas relief. See Fry v. Pliler, 551 U.S. ___, 127 S.Ct. 2321, 2327, 168 L.Ed.2d 16 (June 11, 2007). Section 2254(d) of Title 28, United States Code, provides:
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.
"A state court's decision is `contrary to . . . clearly established Federal law' `if the state court applies a rule that contradicts the governing law set forth in [the Supreme *756 Court's] cases,' or `if the state court confronts facts that are materially indistinguishable from a relevant Supreme Court precedent and arrives at a result opposite to [the Supreme Court's decision].'" Bell v. Cone, 543 U.S. 447, 452-53, 125 S.Ct. 847, 160 L.Ed.2d 881 (2005) (per curiam) (quoting Williams v. Taylor, 529 U.S. 362, 405, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000)). "A state-court decision involves an unreasonable application of [the Supreme] Court's clearly established precedents if the state court applies [the Supreme] Court's precedents to the facts in an objectively unreasonable manner." Brown v. Payton, 544 U.S. 133, 141, 125 S.Ct. 1432, 161 L.Ed.2d 334 (2005) (citing Williams, 529 U.S. at 405). To be unreasonable, the state court's application of Supreme Court precedent must have been "objectively unreasonable," a standard that is more demanding than simply being "incorrect or erroneous." Wiggins v. Smith, 539 U.S. 510, 520-21, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003).
A. State Post-Conviction Proceeding and Motion to Recall
Bell-Bey argues two errors. First, Bell-Bey contends the Missouri Court of Appeals, in Bell-Bey's state post-conviction proceeding, erred by applying the wrong harmless-error standard regarding the admission of hearsay evidence. An application for a writ of habeas corpus can be granted if a prisoner is "in custody pursuant to the judgment of a State court only on the ground that he is in custody in violation of the Constitution or laws or treaties of the United States." 28 U.S.C. § 2254(a). Because the Constitution does not guarantee the existence of state post-conviction proceedings, see Pennsylvania v. Finley, 481 U.S. 551, 557, 107 S.Ct. 1990, 95 L.Ed.2d 539 (1987), "an infirmity in a state post-conviction proceeding does not raise a constitutional issue cognizable in a federal habeas [application]." Williams-Bey v. Trickey, 894 F.2d 314, 317 (8th Cir.1990). Any error in Bell-Bey's state post-conviction proceeding is not a constitutional error that could justify granting an application for a writ of habeas corpus.
Second, Bell-Bey contends the admission of hearsay evidence violated the Confrontation Clause. Bell-Bey never presented this argument to the state court in his motion for post-conviction relief, rather Bell-Bey presented this argument in a motion to recall the mandate in Bell-Bey II. An application for a writ of habeas corpus can only be granted if the applicant has exhausted all of the available state court remedies. See 28 U.S.C. § 2254(b)(1)(A); Jolly v. Gammon, 28 F.3d 51, 53-54 (8th Cir.1994). "[A] motion [] to recall the mandate [was] neither an appropriate nor adequate means of exhausting state remedies." Williams v. Wyrick, 763 F.2d 363, 365 (8th Cir.1985) (per curiam). Bell-Bey has not exhausted all the available state court remedies, and has not established any cause for the default and actual prejudice or shown actual innocence to excuse the default. See Cagle v. Norris, 474 F.3d 1090, 1099 (8th Cir. 2007). Thus, Bell-Bey's application for a writ of habeas corpus cannot be granted.
B. Batson Challenge
Bell-Bey contends the state court's ruling on the Batson challenge was contrary to and an unreasonable application of clearly established federal law. During voir dire, both the trial court and the state attorney instructed jurors to treat the credibility of police officers in the same manner as the credibility of lay persons. Minutes later, Bell-Bey's counsel questioned veniremember Johnson:
[Bell-Bey's counsel]: Mr. Johnson, is there anything about a police officer that would tend to make you believe a police officer more than any other witness?

*757 [Veniremember Johnson]: No.
The state attorney then struck five of seven African-American veniremembers, including veniremember Johnson, the only male African-American veniremember. Bell-Bey challenged the state attorney's use of peremptory strikes pursuant to Batson. The state attorney claimed nondiscriminatory reasons for striking veniremember Johnson, specifically stating "[veniremember Johnson] stated extremely firmly that he absolutely believed police officers can lie. I would say based on that and body language toward me as opposed to [Bell-Bey's counsel], that I did not believe that he would be a pro-state juror." The trial court found the state attorney's proffered rationale was race neutral and overruled Bell-Bey's Batson challenge.
The Equal Protection Clause proscribes striking veniremembers on the basis of race. See Batson, 476 U.S. at 85-86. In Rice v. Collins, 546 U.S. 333, 338, 126 S.Ct. 969, 163 L.Ed.2d 824 (2006), the Supreme Court described the Batson challenge procedure:
A defendant's Batson challenge to a peremptory strike requires a three-step inquiry. First, the trial court must determine whether the defendant has made a prima facie showing that the prosecutor exercised a peremptory challenge on the basis of race. Second, if the showing is made, the burden shifts to the prosecutor to present a race-neutral explanation for striking the juror in question. Although the prosecutor must present a comprehensible reason, the second step of this process does not demand an explanation that is persuasive, or even plausible; so long as the reason is not inherently discriminatory, it suffices. Third, the court must then determine whether the defendant has carried his burden of proving purposeful discrimination. This final step involves evaluating the persuasiveness of the justification proffered by the prosecutor, but the ultimate burden of persuasion regarding racial motivation rests with, and never shifts from, the opponent of the strike.
Id. (internal alterations, citations, and quotation marks omitted). We presume the correctness of and defer to the trial court's factual findings regarding the persuasiveness of the rationale for using a peremptory strike. See Miller-El v. Cockrell, 537 U.S. 322, 339-40, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003); Purkett v. Elem, 514 U.S. 765, 769, 115 S.Ct. 1769, 131 L.Ed.2d 834 (1995) (per curiam).
Here, the trial court assumed Bell-Bey had made a prima facie showing pursuant to Batson, listened to the state attorney's rationale for using a peremptory strike on veniremember Johnson, and overruled Bell-Bey's Batson challenge. Bell-Bey argues the Batson challenge was decided in a manner that is contrary to federal law because the trial court did not consider whether the state attorney's rationale was merely a pretext for striking veniremember Johnson. The trial court explicitly found the state attorney's rationale for striking veniremember Johnson to be credible. Nothing in the record suggests the trial court "failed to assess whether the reason offered by the [state] to strike this veniremember was a valid race neutral reason." United States v. Carter, 481 F.3d 601, 610 (8th Cir.) (affirming the overruling of a Batson challenge on direct appeal), petition for cert. filed (U.S. July 11, 2007) (No. 07-5323). The Missouri Court of Appeals concluded "[Bell-Bey] did not demonstrate that the reason was pretextual and that the strike was racially motivated." Although the trial court could have expressly requested argument from Bell-Bey's counsel before ruling on the Batson challenge, the trial court's conclusion the state attorney's nondiscriminatory rationale was persuasive *758 (without further argument) was not contrary to clearly established federal law. Clearly established federal law dictates the prosecutor's explanation need not be "persuasive, or even plausible; so long as the reason is not inherently discriminatory," Rice, 546 U.S. at 338 (internal quotation marks omitted), and when the trial court makes the necessary credibility determination, we defer to that ruling and there is "nothing left to review," Miller-El, 537 U.S. at 339-40 (internal quotation marks omitted).
Bell-Bey also argues the trial court unreasonably applied clearly established federal law by allowing the state attorney to strike veniremember Johnson. The state attorney offered two reasons, specifically, the statement police officers could lie and veniremember Johnson's body language, to explain the decision to strike veniremember Johnson. The record does not support the first reason. Veniremember Johnson replied to the question according to the instructions given by the trial court and the state attorney. Nonetheless, the state attorney offered veniremember Johnson's body language as a second reason for the strike. "[A] juror's demeanor and body language may serve as legitimate, race-neutral reasons to strike a potential juror." United States v. Maxwell, 473 F.3d 868, 872 (8th Cir.), cert. denied, ___ U.S. ___, 127 S.Ct. 2292, 167 L.Ed.2d 1121 (2007). The trial court found this rationale to be persuasive and "was in the best position to evaluate the [state's] credibility." Id. Assuming for the purpose of argument that the state attorney's first reason gives rise to some inference of discrimination, this inferred discrimination is nevertheless insufficient because the state attorney also provided a nondiscriminatory reason for the use of the peremptory strike. See Weaver v. Bowersox, 241 F.3d 1024, 1032 (8th Cir.2001) (denying an application for a writ of habeas corpus based on a Batson challenge when the state attorney had articulated both discriminatory and nondiscriminatory reasons for the use of the peremptory strike).
Bell-Bey complains the trial court never developed the factual basis of veniremember Johnson's body language and never allowed Bell-Bey's counsel to challenge the state attorney's rationale. The burden, however, rested on Bell-Bey to rebut and develop a record demonstrating the state attorney's proffered nondiscriminatory rationale for the peremptory strike was pretextual. See Rice, 546 U.S at 338; United States v. Jones, 245 F.3d 990, 993-94 (8th Cir.2001); see also Smulls v. Roper, 467 F.3d 1108, 1117 (8th Cir. 2006) (Hansen, J., concurring in part and dissenting in part) (stating "the trial court fulfills its `duty to rule' on the Batson third-step analysis `by expressing a clear intent to uphold or reject a strike after listening to the challenge, the race-neutral explanation, and the arguments of the parties'" (quoting Messiah v. Duncan, 435 F.3d 186, 189 (2d Cir.2006))), vacated & reh'g en banc granted, No. 05-2456 (8th Cir. Feb. 2, 2007). The trial court listened to and considered Bell-Bey's argument both before and after overruling Bell-Bey's Batson challenge. Cf. United States v. Feemster, 98 F.3d 1089, 1091 (8th Cir. 1996) (concluding the trial court had adequately completed the third step of a Batson challenge by weighing the persuasiveness of the proffered nondiscriminatory rationale and by making a finding the government had not exercised a peremptory strike in a discriminatory manner). We defer to the factual findings of the trial court regarding the persuasiveness of the state attorney's nondiscriminatory rationale for striking veniremember Johnson and conclude the overruling of Bell-Bey's Batson challenge was not an unreasonable application of federal law. See Miller-El, 537 U.S. at 339-40.
*759 C. Admission of Business Records
Bell-Bey complains the district court violated the Due Process and Compulsory Process Clauses by excluding certain business records and testimony about what was not in the records. "Questions regarding admissibility of evidence are matters of state law, and they are reviewed in federal habeas inquiries only to determine whether an alleged error infringes upon a specific constitutional protection or is so prejudicial as to be a denial of due process." Rousan v. Roper, 436 F.3d 951, 958 (8th Cir.) (quotation omitted), cert. denied, ___ U.S. ___, 127 S.Ct. 68, 166 L.Ed.2d 60 (2006). The trial court traditionally has broad discretion when it comes to determining relevancy and admissibility. See Pfau v. Ault, 409 F.3d 933, 940 (8th Cir.2005). The Supreme Court of Missouri concluded Bell-Bey's proffered business records and testimony were only marginally relevant and the trial court did not abuse its discretion by excluding the evidence. A trial court may exclude the defendant's evidence on grounds the evidence is only marginally relevant without violating the Constitution. See Garcia, 474 F.3d at 1017-18 (citing Holmes v. South Carolina, 547 U.S. 319, 326-27, 126 S.Ct. 1727, 164 L.Ed.2d 503 (2006)). The exclusion of marginally relevant evidence is not an unreasonable application of federal law. Bell-Bey's constitutional Due Process and Compulsory Process Clause rights were not violated by the exclusion of the business records and related testimony.
III. CONCLUSION
We affirm the judgment of the district court.
NOTES
[1]  The Honorable E. Richard Webber, United States District Judge for the Eastern District of Missouri, adopting the report and recommendation of the Honorable Lewis M. Blanton, United States Magistrate Judge for the Eastern District of Missouri.
