Ray Dansby was convicted by a jury in Arkansas on two counts of capital murder and sentenced to death. The district court denied his application for a writ of habeas corpus. Dansby initially appealed on five claims covered by a certificate of appeala-bility, and asked this panel to expand the certificate with respect to four other claims. After we filed our opinion on that appeal, Dansby petitioned the Supreme Court for a writ of certiorari. The Court granted certiorari, vacated our judgment, and remanded for further consideration in light of Trevino v. Thaler, — U.S.-, 133 S.Ct. 1911, 185 L.Ed.2d 1044 (2013). See Dansby v. Hobbs, — U.S.-, 133 S.Ct. 2767, 186 L.Ed.2d 215 (2013). We expanded the certificate of appealability to include all claims that the district court ruled were procedurally defaulted. We now affirm in part, vacate the dismissal of Claims II and III in Dansby’s second amended petition, and remand for further proceedings.
I. ■
As summarized by the Arkansas Supreme Court, see Dansby v. State, 319 Ark. 506, 893 S.W.2d 331 (1995), the evidence at trial showed that on the morning of August 24, 1992, Dansby arrived at the residence of Brenda Dansby, his ex-wife, in El Dorado, Arkansas. Justin Dansby, their nine-year-old son, was in the living room with Ronnie Kimble, Brenda’s boyfriend. Justin was home with a cold and watching television, while Kimble was asleep on the couch. Brenda had left earlier to buy orange juice for Justin, and when she returned home, she was confronted by Ray as she pulled her car into her driveway. Ray twice ordered her to leave her car, and she eventually complied. Justin testified at trial that he saw Ray hold Brenda “like a shield” before shooting her in the arm and in the neck.
Greg Riggins, a neighbor from across the street, also offered an account of Brenda’s death. According to his trial testimony, Riggins went to his front door after hearing gunshots and witnessed Ray and Brenda struggling with a revolver. He then saw Ray knock Brenda down, get the gun from her, and shoot two consecutive rounds into her from two or three feet away. Brenda tried to rise, and Ray fired again, although Riggins believed the shot missed. After pausing for five or six seconds, Ray shot Brenda once more, and her body went flat.
Justin testified that Ray then entered the home and shot Kimble in the chest, at which point Kimble got his own gun from beneath the couch. Kimble positioned *815himself behind the couch and attempted to return fire, but his gun only produced “clicking sounds.” Ray chased Kimble to the back of the house, and Justin heard about five more shots. When Justin went to investigate, he saw his father standing over Kimble, kicking him twice and then saying something Justin could not remember. Justin accompanied his father outside the house, where he saw his mother, motionless, with “blood all over her neck.” Ray and Justin walked down the road, and after they separated, Justin called the police.
El Dorado police officers arrived at Brenda’s home to find her body outside. They also found an injured Kimble on the floor of the back bedroom, along with a jammed .38 automatic pistol lying under him. Kimble eventually died of his wounds at a local hospital, but not before telling a police detective that Ray Dansby had shot him.
Later the same day, Officer Mike Ste-gall came upon Ray Dansby, who said, “I’m Ray Dansby, ya’ll are looking for me.” Stegall asked Dansby whether he was carrying any guns, and Dansby answered that he had thrown them away. Stegall then took Dansby to the police station, where Lieutenant Mike Hill advised him of his rights. Dansby stated that he had left the scene with two guns, a .32 revolver and a .38 revolver, but had disposed of them where the police would never find them. By Dansby’s account of the day’s events, he had armed himself before traveling to Brenda’s home because he knew both she and Kimble had handguns. Dansby explained that he had entered the front door to Brenda’s home to find Kim-ble holding a handgun in his right hand “pointed down,” and Dansby stated that after an argument ensued, “I just pulled my gun and started shooting.” After making these statements, Dansby submitted to a gunshot residue test and signed a written rights waiver form, but he declined to provide a tape-recorded statement.
At trial, prosecutors presented several pieces of evidence beyond the eyewitness testimony of Justin Dansby and Greg Rig-gins. The autopsy revealed gunshot wounds near Brenda’s left ear and on her upper chest; similar wounds were found on Kimble’s chest, right arm, and left upper back, behind his left ear, and superficial wounds were present on his left flank. The jury also heard testimony that Dansby was scheduled to appear in court on charges of second-degree assault and contempt of court at 9:00 a.m. on the day of the murders, and that state prosecutors brought these charges after Brenda had provided them with a signed affidavit alleging that Dansby had assaulted her.
Also testifying for the prosecution was Dansby’s jail cellmate Larry McDuffie, the boyfriend of Dansby’s half-sister. McDuf-fie said Dansby admitted in jail that he had murdered Kimble and Brenda. According to McDuffie, Dansby told him he was “just glad” that Brenda was dead. McDuffie also testified that in response to Brenda’s pleas for mercy, Dansby answered, “well b- you done f- up cause I’m not gonna leave you out here in these streets when I done killed this man inside.”
An Arkansas jury convicted Dansby of two counts of capital murder on June 11, 1993, and sentenced him to death by lethal injection on both counts. The Arkansas Supreme Court affirmed the conviction and sentence. Dansby, 893 S.W.2d at 331. Dansby petitioned for postconviction relief under Arkansas Rule of Criminal Procedure 37, claiming ineffective assistance of counsel. The trial court denied the petition, and the Arkansas Supreme Court affirmed. Dansby v. State, 350 Ark. 60, 84 S.W.3d 857 (2002).
*816Pursuant to 28 U.S.C. § 2254, Dansby filed a petition for a writ of habeas corpus in the district court. The district court denied relief on all claims and dismissed the petition. The court then denied Dans-by’s motion to alter or amend the judgment. Dansby sought a certificate of ap-pealability, and the district court granted a certificate on three claims: that Dansby is actually innocent of the murders of Brenda and Kimble, that improper testimony at trial about Dansby’s postarrest silence violated his constitutional rights, and that the evidence offered at trial was insufficient to establish premeditation and deliberation. An administrative panel of this court expanded the certificate of appealability to include Dansby’s claims that the State failed to disclose material, exculpatory evidence concerning witness Larry McDuffie, and that the trial court impermissibly limited impeachment of McDuffie at trial in violation of Dansby’s rights under the Confrontation Clause. After the Supreme Court’s remand, we expanded the certificate of appealability to encompass all claims the district court had determined to be procedurally defaulted and requested supplemental briefing.
II.
A.
Dansby’s broadest claim (Claim I of the second amended petition) is that new evidence discovered after trial shows that he is actually innocent of murder. On that basis, he argues that the conviction and sentence violate his rights under the Eighth Amendment. Dansby says the new evidence — including documents allegedly withheld by the State and a statement in which prosecution witness McDuffie purportedly recants his trial testimony — • would allow him to impeach McDuffie’s credibility and establish that Dansby acted in lawful self-defense when he killed Brenda and Kimble.
The Supreme Court has not decided whether a persuasive demonstration of actual innocence after trial would render unconstitutional a conviction and sentence that is otherwise free of constitutional error. See House v. Bell, 547 U.S. 518, 554-55, 126 S.Ct. 2064, 165 L.Ed.2d 1 (2006). The Court has established, however, that the threshold for any such claim, if it were recognized, would be “extraordinarily high.” Herrera v. Collins, 506 U.S. 390, 417, 113 S.Ct. 853, 122 L.Ed.2d 203 (1993). The threshold, if it exists, would require “more convincing proof’ than the “gateway” standard that allows for consideration of otherwise defaulted constitutional claims upon a showing of actual innocence. House, 547 U.S. at 555,126 S.Ct. 2064; see Schlup v. Delo, 513 U.S. 298, 315, 115 S.Ct. 851, 130 L.Ed.2d 808 (1995). Thus, on a freestanding claim of actual innocence, it is not sufficient that a petitioner shows even that it is “more likely than not that no reasonable juror would have found petitioner guilty beyond a reasonable doubt.” Id. at 327, 115 S.Ct. 851. The “extraordinarily high” threshold, if recognized, would be even higher. House, 547 U.S. at 555, 126 S.Ct. 2064.1
In its order denying relief, the district court treated this claim as a challenge to the sufficiency of the evidence. When Dansby argued in a motion to alter or *817amend the judgment that the court misconstrued his claim, the court explained that if it had reached a freestanding actual innocence claim on the merits, then the claim would have failed. The court reasoned that the only evidence proffered in support of actual innocence was impeachment evidence regarding prosecution witness McDuffie, and that a jury could have believed McDuffie even with the new evidence. The court also said that the new evidence, at most, might have established reasonable doubt, but it could not show that no reasonable juror would have found Dansby guilty. There was ample other evidence that negated Dansby’s claim of self-defense, the court observed, and it would not have been unreasonable for a juror to reject Dansby’s defense even without McDuffie’s testimony.
We, too, conclude that Dansby’s proffered evidence does not meet the extraordinarily high threshold that might support relief based on a showing of actual innocence. As the district court observed, much of the new evidence is designed to undermine the credibility of prosecution witness McDuffie. Latter-day impeachment evidence, however, “will seldom, if ever,” make a clear and convincing case that no reasonable jury could believe the core of the witness’s account. Sawyer v. Whitley, 505 U.S. 333, 349, 112 S.Ct. 2514, 120 L.Ed.2d 269 (1992). Here, moreover, we agree with the Arkansas Supreme Court that there was substantial evidence apart from McDuffie’s testimony that permitted a jury to infer that Dansby killed the victims in a premeditated and deliberate manner. Dansby, 893 S.W.2d at 336. The alleged new evidence cited by Dansby with regard to witnesses other than McDuffie, App. A16-A20, does not compel a conclusion that Dansby acted in lawful self-defense. Some of these facts might be disbelieved or discounted by a reasonable juror; others can be reconciled reasonably with the prosecution’s theory of the case. Dansby’s submission of new evidence would not meet an extraordinarily high threshold for proof of innocence. The district court thus did not err in rejecting this claim without a hearing.
B.
Dansby also contends that the evidence at trial was insufficient to show that he murdered Brenda and Kimble with premeditation and deliberation. This is Claim XIV of the second amended petition. Dansby raised a challenge to the sufficiency of evidence on direct appeal, and the Arkansas Supreme Court rejected it. The Arkansas court said “[t]he test for determining the sufficiency of the evidence is whether there is substantial evidence to support the verdict,” 893 S.W.2d at 335, and ultimately concluded that the evidence of premeditation and deliberation was “overwhelming.” Id. at 336. Where the state court has adjudicated a constitutional claim on the merits, a petitioner must demonstrate that the state court’s decision was “contrary to, or involved an unreasonable application of, clearly established Federal law.” 28 U.S.C. § 2254(d)(1).
Dansby argues for the first time on appeal that § 2254(d) does not apply. He contends that the Arkansas court did not adjudicate his constitutional claim on the merits, but instead resolved the sufficiency-of-evidence contention on state-law grounds only. He points out that the state court applied a “substantial evidence” standard, which this court once said is “arguably different than the due-process standard enunciated” in Jackson v. Virginia, 443 U.S. 307, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979). See Nance v. Norris, 392 F.3d 284, 289 (8th Cir.2004). Jackson held that the Due Process Clause forbids a conviction when “no rational trier of fact *818could have found proof of guilt beyond a reasonable doubt.” 443 U.S. at 324, 99 S.Ct. 2781.
We believe that Dansby’s constitutional claim was adjudicated on the merits, and that the deferential standard of § 2254(d) applies. Unlike Nance v. Norris, where the state court “specifically disclaimed] addressing constitutional arguments,” 392 F.3d at 289, the Arkansas Supreme Court did no such thing in Dansby’s direct appeal. In prior decisions, the Arkansas court has explained its view that the substantial-evidence standard applied in Arkansas cases is consistent with Jackson:
The substantial-evidence standard, while not explicitly reciting the standard from Jackson word for word, requires that evidence supporting a conviction must compel reasonable minds to a conclusion, and force or induce the mind to pass beyond suspicion or conjecture, and, thereby, ensures that the evidence was convincing to a point that any rational fact-finder could have found guilt beyond a reasonable doubt.
Williams v. State, 351 Ark. 215, 91 S.W.3d 54, 61 (2002) (emphasis added) (internal citations omitted). There is thus no reason to believe that the Arkansas Supreme Court in Dansby’s direct appeal adjudicated only a state-law claim while leaving the constitutional due process claim unaddressed. The court adjudicated the two claims together.
Viewing the evidence in the light most favorable to the State, the state court reasoned as follows:
Although the testimony is at variance among different witnesses as to the exact sequence of events during the shootings, there was much said as to the weapons used, and as to the nature, extent, and location of Ms. Dansby’s and Mr. Kimble’s wounds. With reference to the shots fired into Brenda, Dr. Per-etti testified that he located gunshot wounds near the left ear and upper chest of her body. Greg Riggins, an eye witness to Brenda’s murder, testified as to Ray’s hesitation of several seconds before he fired the final shot into Brenda’s head. In observance of the wounds to Ronnie’s body, Dr. Peretti testified that Ronnie sustained wounds to the left ear, chest, left upper back, and right arm, as well as two superficial wounds to the left flank. Particularly, it was Dr. Peretti’s opinion that the wound to Ronnie’s back occurred when he was “probably bent over.” Ray’s son Justin, another eye witness, testified that he watched as his father kicked Ronnie twice, and that he heard his father say something after shooting him. In light of this testimony, the jury could have easily inferred that Dansby fired multiple shots into both victims in a premeditated and deliberated manner.
Dansby, 893 S.W.2d at 336. After considering Larry McDuffie’s testimony that Dansby admitted to planning the murders, the court viewed the evidence as “overwhelming.” Id.
We conclude that the decision of the Arkansas Supreme Court was not contrary to, or an unreasonable application of, Jackson. It is not necessary for the state court to cite the relevant Supreme Court precedent, see Early v. Packer, 537 U.S. 3, 8, 123 S.Ct. 362, 154 L.Ed.2d 263 (2002) (per curiam), so long as the decision satisfies the criteria of § 2254(d). The Arkansas court concluded that the evidence was “of sufficient force and character to compel reasonable minds to reach a conclusion and pass beyond suspicion and conjecture.” Dansby, 893 S.W.2d at 336. This was not an unreasonable way for a state court to ensure that a rational trier of fact could have found the requisite elements beyond a reasonable doubt. The evidence here *819surpassed the constitutional threshold with room to spare. The district court properly rejected Dansby’s due process claim based on sufficiency of the evidence.
C.
Dansby next appeals the district court’s denial of relief on his claim (Claim VI) that improper testimony and comment on his postarrest silence violated his right to due process under the Fourteenth Amendment. The claim arises from the following testimony at trial by Lieutenant Mike Hill of the El Dorado Police Department.
COUNSEL FOR STATE: Did [Dans-by] appear to understand his rights as you verbally advised ...
WITNESS: Yes.
COUNSEL FOR STATE: ... him of them?
WITNESS: Yes, he did.
COUNSEL FOR STATE: And did you have a conversation with him about these events at all?
WITNESS: Yes, after I informed him, of course, that he had the right to remain silent. Anything he said could be used against him in a court of law, and that, you know, if he wanted a lawyer present during questioning he could have one. And I asked him if he understood that at any time, you know, that he didn’t wish to talk any longer he didn’t have to.
I said or I asked him it’s very important that we find this gun. I said anyone could pick this gun up. What did you do with it? At that point he began to tell me that he left the scene with two guns, a .32 and a .38, both revolvers. And that he threw them away where we would never find ‘em and he wasn’t worried about anybody finding ‘em.
After obtaining the gunshot residue kit, I sat down at my desk and again informed him of his rights. This time I read to him his rights from the standard waiver form that we use which he again acknowledged that he understood and signed the form.
COUNSEL FOR STATE: I’ll show you what’s been marked previously as State’s Exhibit No. 2, and ask you if you can identify this, please [handing to witness].
WITNESS: Yes, this is the form that I read to Ray Dansby that morning. It’s noted here at the top 9:00 a.m., at the bottom 9:14 a.m. which would have been the time that I read directly to him from the form and that he signed it. COUNSEL FOR STATE: Okay. And then at some point did he also decline to talk?
WITNESS: Yes, at 9: ...
COUNSEL FOR DEFENDANT: Objection.
WITNESS: ...21 a.m.
COUNSEL FOR DEFENDANT: Objection.
THE COURT: What’s your objection? COUNSEL FOR DEFENDANT: May we approach?
Trial R. 803-04 (emphases added).
At a bench conference, Dansby’s counsel objected that it was impermissible for Hill to refer to Dansby’s invocation of his right to remain silent. She moved for a mistrial. The trial court did not hear Hill “say anything about anybody invoking anything,” and denied the motion for mistrial. Id. at 805. The court directed the prosecution to admonish Hill that he should not “make any reference or comment about any rights being invoked or about the defendant refusing to answer questions.” Id. at 808. And the court directed the prosecution to redact an advice-of-rights form *820signed by Dansby to remove a notation about his invocation of the right to remain silent. Id. at 808. The court then inquired whether Dansby wanted the court to admonish the jury “just in case something slipped through,” but Dansby said through counsel that he did not want an admonishment. Id. at 808-09.
On direct appeal, Dansby argued that Hill’s answer that “Yes,” Dansby did decline to talk at some point during the interview, violated Dansby’s due process rights as construed in Doyle v. Ohio, 426 U.S. 610, 96 S.Ct. 2240, 49 L.Ed.2d 91 (1976). Doyle held that when an accused invokes his right to remain silent after receiving advice about his rights pursuant to Miranda v. Arizona, 384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966), the Constitution forbids the prosecution to use the accused’s silence to impeach his testimony at a later trial. 426 U.S. at 619, 96 S.Ct. 2240. The Court reasoned that the Miranda warnings carry an implicit assurance that “silence will carry no penalty,” and that “it would be fundamentally unfair and a deprivation of due process to allow the arrested person’s silence to be used to impeach an explanation subsequently offered at trial.” Id. at 618, 96 S.Ct. 2240.
The Arkansas Supreme Court rejected Dansby’s claim. The court concluded that “the testimony elicited from Lieutenant Hill was not a comment on Dansby’s right to remain silent; rather, it merely explained to the jury why there was not a taped statement.” 893 S.W.2d at 340-41. Earlier in the trial, Mike Stegall, another police officer who participated in Dansby’s interrogation, testified that “after [Dans-by] had given us his statement ... Lieutenant Hill advised him that we needed to turn the tape recorder on to record his statement. At which point Mr. Dansby invoked his rights and stated that he didn’t want to say anything else without a lawyer.” Trial R. 676. The Arkansas court evidently believed that Hill’s answer, like Stegall’s testimony, explained why there was no recording of Dansby’s admissions, and that such testimony did not violate Dansby’s due process rights.
Because the Arkansas Supreme Court resolved the Doyle claim on the merits, Dansby is entitled to relief only if the state court’s decision was “contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States.” 28 U.S.C. § 2254(d)(1). The district court concluded that he could not meet that standard. The court ruled alternatively that any error was harmless.
Dansby contends that the Arkansas court’s decision was an unreasonable application of Doyle and Wainwright v. Greenfield, 474 U.S. 284, 106 S.Ct. 634, 88 L.Ed.2d 623 (1986). Dansby cites Greenfield’s holding that the prosecution could not use an accused’s post -Miranda warning silence to overcome a defendant’s plea of insanity, because the implicit promise, breach, and consequent penalty is the same in that situation as when the prosecution seeks to use silence to impeach the accused’s testimony at trial. 474 U.S. at 292, 106 S.Ct. 634. Dansby argues that the State impermissibly used his silence to rebut an inference that Lieutentant Hill was fabricating Dansby’s unrecorded statement about guns, and that the state court unreasonably applied Greenfield and Doyle by permitting Hill’s testimony that Dansby invoked his right to remain silent.
This court has concluded that not every reference to an accused’s post-Miranda warning silence violates due process. In Mathenia v. Delo, 975 F.2d 444 (8th Cir. 1992), a law enforcement officer testified that he advised an arrestee of his rights, but that the arrestee did not make a statement at the time of his arrest. Other *821evidence showed that the arrestee made a videotaped statement two weeks later. This court, agreeing with the state court in that case, held that the officer’s testimony was “ ‘merely preliminary to the admission into evidence of [the arrestee’s] videotaped statement.’ ” Id. at 452 (quoting State v. Mathenia, 702 S.W.2d 840, 842 (Mo.1986)). Evidence that the accused did not make a statement at the time of arrest “merely crystalized what was already suggested by the fact that appellant ultimately did make a statement” at a later date. State v. Mathenia, 702 S.W.2d at 842; cf. Greer v. Miller, 483 U.S. 756, 763, 107 S.Ct. 3102, 97 L.Ed.2d 618 (1987) (“[T]he holding of Doyle is that the Due Process Clause bars the use for impeachment purposes of a defendant’s postarrest silence.”) (internal quotation omitted).
The Supreme Court has not addressed a case like Mathenia. The line between permissible references to postarrest silence for explanatory purposes and impermissible breaches of the implied Miranda-warning promise, therefore, must emerge from case-by-case applications of Doyle over a period of time. In the meantime, state courts have some leeway to reach reasonable judgments in this area. See Yarborough v. Alvarado, 541 U.S. 652, 663-64, 124 S.Ct. 2140, 158 L.Ed.2d 938 (2004). It was not an unreasonable application of Supreme Court precedent for the Arkansas court to conclude that Hill’s answer in this case was permissible. Officer Stegall already had testified without objection that the officers attempted to tape record Dansby’s statement, but that Dans-by declined to say anything more. Hill’s testimony that Dansby declined at some point to speak further could reasonably be viewed by a state court merely as an explanation of the circumstances of Dansby’s interview, not as a penalty for invoking the right to remain silent.2
D.
Dansby’s fourth point on appeal is that the district court erroneously rejected his claim that the state trial court denied his right under the Sixth Amendment to confront a witness against him, Larry McDuf-fie. This is Claim II in the second amended petition.
After Dansby was arrested for murder, he was incarcerated with McDuffie in Union County, Arkansas. McDuffie was in jail after his arrest on a pending felony drug charge. Before trial, the prosecution moved in limine for an order to preclude the defense from “mentioning or attempting to elicit testimony from any witness regarding the reason for McDuffie’s incarceration, and pending charges or related matters.” The trial court ruled that charges that had been filed in the past against McDuffie that did not result in convictions “are clearly inadmissible and should not be referred to because the witness may not be impeached in that manner.” Trial R. 636. The court provided that Dansby could inquire whether McDuf-fie had served as a confidential informant for the El Dorado police department and whether he had been paid by that agency for information in the past. Id. at 248.
Dansby’s counsel sought additional leeway to elicit testimony designed to show McDuffie’s bias. In a memorandum brief and at a pretrial hearing, counsel asserted that McDuffie had a history of working as an informant for the State, that he had been in and out of jail three or four times *822in recent months, that the State’s treatment of previous criminal cases against him was inconsistent with its handling of other cases, that he was not sanctioned for violating conditions of release, and that evidence of these events would show McDuffie’s bias toward the State. Id. at 296-97, 631-32.
The court ordered that Dansby could inquire whether McDuffie had received promises of leniency or guarantees of immunity, but could not present evidence about “extrinsic matters which would call upon the jury to perform a feat of speculation or conjecture in order to relate it to [the] alleged bias.” Id. at 637. The court ruled that unless there was “direct evidence of an agreement of a promise of immunity or something along that nature, ... you’re in the realm of speculation and conjecture.” Id. at 638. The oral ruling concluded as follows: “I’m going to grant the motion in limine as to argument about and statement about these charges and then just allow the matter to proceed as to these other areas.” Id. at 640. During cross-examination of McDuffie, the court sustained an objection to defense counsel’s question about why McDuffie was held in jail at the time of his statement to police about Dansby. Id. at 907. Before the case was submitted to the jury, Dansby made a proffer of evidence that he sought to use to show McDuffie’s alleged bias. Id. at 969-89.
On direct appeal, Dansby challenged the trial court’s restrictions on cross-examination, arguing in part that McDuffie’s “past dealing with law enforcement, including all the surrounding circumstances of his past criminal record and the penalties or rewards he received, were relevant to the jury’s consideration of the testimony he would give at the trial.” Dansby urged, among other things, that the trial court’s right to limit testimony “must be weighed against the defendant’s confrontation rights and fair trial rights guaranteed by the Sixth Amendment.” The Arkansas Supreme Court concluded that Dansby’s proffered evidence was “not relevant to show bias,” and upheld the trial court’s ruling. 893 S.W.2d at 339. The state supreme court opined that Dansby had not proffered direct evidence of an agreement or promise of immunity, and that a jury could not have made a connection between McDuffie’s arrests and his alleged bias in the Dansby trial without speculation or conjecture. Id.
In his federal habeas petition, Dansby challenged the trial court’s ruling as a violation of his rights under the Sixth Amendment. Dansby complained that the ruling unconstitutionally precluded him from cross-examining McDuffie and from introducing extrinsic evidence to expose his bias and motive to fabricate. But cf. Driver v. Landers, 444 Fed.Appx. 934, 936 (9th Cir.2011) (“The Supreme Court has never held that the Confrontation Clause requires, in addition to cross-examination, the admission of extrinsic evidence for the purpose of establishing a witness’s motive to lie.”); Brown v. Ruane, 630 F.3d 62, 70-71 (1st Cir.2011) (“[T]he Supreme Court’s Confrontation Clause jurisprudence left a defendant’s right to introduce extrinsic impeachment evidence as an open constitutional question.”).
The district court dismissed this claim on the ground that it was procedurally defaulted. The court concluded that Dans-by never presented a claim of federal constitutional error in his direct appeal to the state supreme court, and that the claim was therefore defaulted. See O’Sullivan v. Boerckel, 526 U.S. 838, 848, 119 S.Ct. 1728, 144 L.Ed.2d 1 (1999). The district court noted that Dansby’s brief on direct appeal included one mention of the Sixth Amendment, but reasoned that Dansby failed to *823assert that the trial court’s ruling violated his federal constitutional rights.
Dansby argues that he fairly presented a federal constitutional argument to the state supreme court, and we agree. To exhaust a claim properly in state court, a prisoner must give the state courts a fair opportunity to act on the claim. Id. at 844, 119 S.Ct. 1728. A petitioner must present “ ‘both the factual and legal premises’ ” of his claims to the state courts in order to exhaust the claims properly. Flieger v. Delo, 16 F.3d 878, 884 (8th Cir.1994) (quoting Cox v. Lockhart, 970 F.2d 448, 454 (8th Cir.1992)). The legal aspect of this requirement is satisfied if the petitioner’s argument to the state court “refer[s] to a specific federal constitutional right, a particular constitutional provision, a federal constitutional case, or a state case raising a pertinent federal constitutional issue.” Abdullah v. Groose, 75 F.3d 408, 412 (8th Cir.1996) (en banc) (internal quotation omitted).
As noted, Dansby’s brief on direct appeal to the Arkansas Supreme Court argued that limits on impeachment “must be weighed against the defendant’s confrontation rights and fair trial rights guaranteed by the Sixth Amendment.” The brief also cited Sullivan v. State, 32 Ark. App. 124, 798 S.W.2d 110 (1990), for the proposition that “[e]videnee of guarantees of immunity or promises of leniency or any other considerations are a proper subject for cross examination.” As authority for this same point, Sullivan cited Delaware v. Van Ars-dall, 475 U.S. 673, 106 S.Ct. 1431, 89 L.Ed.2d 674 (1986), a decision that addressed the requirements of the federal Confrontation Clause. Id. at 679, 106 S.Ct. 1431. Dansby’s specific invocation of the Sixth Amendment and a state court decision that applied the federal constitutional provision, followed by his assertion that the trial court should have allowed him to attack McDuffie’s alleged bias and prejudice in certain ways that the trial court prohibited, was sufficient to give the state supreme court fair notice that he raised a federal constitutional claim in addition to a state-law evidentiary argument. See Snell v. Lockhart, 14 F.3d 1289, 1298-99 (8th Cir.1994).
For these reasons, we conclude that the district court erred in determining that Dansby failed to present a Sixth Amendment claim to the Arkansas Supreme Court. The parties have not addressed the extent to which the factual premises of Dansby’s current federal claim were presented to the state supreme court, so we do not take up that matter. We vacate the dismissal of Claim II and remand the claim to the district court for further consideration.
E.
The final claim on which Dansby initially received a certificate of appealability concerns alleged prosecutorial misconduct. This claim (Claim III) involves two related allegations: (1) that the State violated the rule of Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), by withholding material exculpatory evidence regarding the credibility of McDuffie, and (2) that the State violated Dansby’s right to due process by knowingly permitting McDuffie to testify falsely. See Napue v. Illinois, 360 U.S. 264, 79 S.Ct. 1173, 3 L.Ed.2d 1217 (1959). Dansby contends that the prosecution concealed various unwritten inducements it had offered McDuffie in exchange for his testimony. These inducements included, he asserts, a favorable sentencing recommendation in McDuffie’s pending felony drug case and nonenforcement of the conditions of his probation. Dansby also relies on a statement purportedly signed by McDuffie in 2005, in which he recants his trial testi*824mony and accuses the prosecution of directing him to testify in a manner that he told the authorities was not true.
The district court dismissed Dansby’s Brady-Napue claim on the ground that it was procedurally defaulted. In a motion to alter or amend the judgment, Dansby complained that the court had raised the doctrine of procedural default sua sponte without giving the parties appropriate notice and opportunity to be heard. The district court denied the motion, stating that Eighth Circuit precedent authorized the court to consider default sua sponte, and that “due to the intertwine of Petitioner’s Claims II and III, there was adequate notice of the possibility of procedural default, if any notice was due.” Claim II was the alleged violation of the Confrontation Clause.
A federal court has discretion to address procedural default in a habeas corpus case despite the State’s failure to present the issue properly. King v. Kemna, 266 F.3d 816, 822 (8th Cir.2001). The Supreme Court has held that before a court may address sua sponte a different procedural defense — timeliness of a habeas petition — it must give the parties fair notice and an opportunity to present their positions. See Wood v. Milyard, — U.S. -, 132 S.Ct. 1826, 1834, 182 L.Ed.2d 733 (2012); Day v. McDonough, 547 U.S. 198, 210, 126 S.Ct. 1675, 164 L.Ed.2d 376 (2006). The same requirements of notice and opportunity to be heard should apply when a federal court chooses to address procedural default on its own initiative. See Prieto v. Quarterman, 456 F.3d 511, 518 (5th Cir.2006); Boyd v. Thompson, 147 F.3d 1124, 1128 (9th Cir.1998). The district court did not give the parties such notice and opportunity, but the State asserts that its response to Dansby’s second amended petition adequately raised the issue of procedural default. We disagree.
The State responded to Claim III of the second amended petition, Dansby’s claim based on Brady and Napue, as follows:
This issue was addressed to some degree in the first claim of both the original habeas petition and the first amended habeas petition. The arguments from the prior two responses are incorporated herein, as if fully set forth. To the extent that it was not previously addressed, the issue was correctly decided on the merits by the State Supreme Court. The entire argument regarding issues decided correctly on the merits by the state’s highest court, set out in claim I of this response, is incorporated herein as if fully set forth.
Resp. to Second Am. Pet. for Writ of Habeas Corpus 5.
The first claim in the original petition and the first amended petition was that the state trial court’s ruling on cross-examination of McDuffie violated the Confrontation Clause. In response to the original petition, the State argued that Dansby failed to cite any federal law or to assert constitutional error in state court: “Claim number one was grounded solely in state law, and for that reason is defaulted.” Resp. to Pet. for Writ of Habeas Corpus 5. In response to the Confrontation Clause claim raised in the first amended petition, the State incorporated its original response and reiterated that “[t]his issue was presented on state law grounds only to the Arkansas Supreme Court.” Resp. to First Am. Pet. for Writ of Habeas Corpus 1.
We do not understand how the State’s incorporation of these responses when answering Dansby’s Brady-Napue claim gave notice of its position that the Brady-Napue claim was procedurally defaulted. If the Brady-Napue claim was procedurally defaulted, the default was not occa*825sioned because Dansby argued only state law when challenging the trial court’s limitation on cross-examination of McDuffie. Limitation on cross-examination is an issue distinct from whether the prosecution withheld material exculpatory evidence or knowingly presented false testimony. We conclude, therefore, that the parties were not afforded adequate notice and opportunity to be heard on the issue of procedural default, and the Brady-Napue claim must be remanded for further consideration.
III.
A.
In papers filed after this case was first briefed, argued, and submitted, Dansby urged this panel to expand the certificate of appealability to encompass Claim XVIII, which asserts that the jury arbitrarily refused to consider mitigating evidence in violation of the Eighth Amendment. The district court and an administrative panel of this court denied previous applications on this claim, but Dansby contends that intervening court decisions warrant reconsideration. This panel has authority to expand a certificate of appealability, but we reexamine the action of a prior panel with caution. Watts v. Norris, 356 F.3d 937, 941 (8th Cir.2004). We deny the application to expand the certificate on this issue.
The district court concluded that the Arkansas Supreme Court rejected this claim on the merits, and that the decision was not contrary to or an unreasonable application of clearly established federal law. See 28 U.S.C. § 2254(d). We conclude that Dansby has not made a substantial showing of a denial of a constitutional right. See id. § 2253(c)(2).
Dansby’s contention is based on the jury’s decision to mark Option D on Form 2 of the jury forms. Form 2 was entitled “Mitigating Circumstances.” Option D read: “There was no evidence of any mitigating circumstance.” Option A permitted the jury to list mitigating circumstances that it unanimously found probably existed at the time of the murder; Option B allowed the jury to list mitigating circumstances that one or more members of the jury believed probably existed, but on which the jury was not unanimous; and Option C applied if the jury found that “there was evidence of’ any of six enumerated mitigating circumstances, or any other that the jury might identify, but the jury unanimously agreed that the circumstances did not exist at the time of the murder.
Assuming for the sake of analysis that the claim was fairly presented to the state courts and is not procedurally defaulted, we conclude that Dansby has not made a substantial showing of a denial of a constitutional right. See 28 U.S.C. § 2253(c); Slack v. McDaniel, 529 U.S. 473, 483-84, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000). Dansby suggests that the action of the jury in this case violated the Eighth Amendment as construed in Mills v. Maryland, 486 U.S. 367, 108 S.Ct. 1860, 100 L.Ed.2d 384 (1988). Mills vacated the imposition of a death sentence where the record showed “a substantial probability that reasonable jurors ... well may have thought they were precluded from considering any mitigating evidence unless all 12 jurors agreed on the existence of a particular such circumstance.” Id. at 384, 108 S.Ct. 1860; see also Commonwealth v. Chambers, 570 Pa. 3, 807 A.2d 872, 883 (2002) (finding an Eighth Amendment violation where “the instruction, when read as a whole, seems to indicate to jurors that, once they have unanimously found an aggravating circumstance, before they can weigh aggravating circumstances against any mitigating circumstances, they must *826all find the existence of at least one mitigating circumstance”).
In our view, there is not a substantial showing on this record of an Eighth Amendment violation based on Mills. Option B on the verdict form in this case plainly allowed the jury to list mitigating circumstances that any one juror found probably existed, even when the jury did not find that circumstance unanimously. The instructions and forms thus did not run afoul of the rule stated in Mills.
Dansby appears to propose a different Eighth Amendment rule — namely, that if the defendant submits evidence that he claims to be mitigating, then a failure of the jury to find that there was evidence of a mitigating circumstance violates the Eighth Amendment. Dansby identifies no decision of the Supreme Court of the United States that so holds, and the Arkansas Supreme Court actually rejects the proposition. In Hill v. State, 331 Ark. 312, 962 S.W.2d 762 (1998), the state supreme court held that “ ‘[a] jury is not required to find a mitigating circumstance just because the defendant puts before the jury some evidence that could serve as the basis for finding the mitigating circumstance.’ ” Id. at 764 (quoting Bowen v. State, 322 Ark. 483, 911 S.W.2d 555, 561 (1995)). A jury, the court explained, may reject all or any part of a defendant’s mitigating evidence. Id. In this very case, the state supreme court cited Hill for that point in dismissing Dansby’s claim that his counsel was ineffective at the penalty phase because the jury found no mitigating factors. Dansby, 84 S.W.3d at 862-63. Dansby’s jury was free to reject his proposed mitigating evidence. That the jury marked Option D on the verdict form does not translate into a substantial showing of a constitutional violation.
Dansby directs our attention to Williams v. State, 2011 Ark. 534, 2011 WL 6275536 (Ark.2011), where the Arkansas Supreme Court held that a jury’s decision to check Option D of Form 2 in a capital case was reversible error, because the defendant had presented “unrebutted evidence in mitigation.” Id. at **3. The Arkansas Supreme Court, however, recently overruled Williams “in its entirety,” concluding that it was premised on multiple legal errors. See Nooner v. State, 2014 Ark. 296, 438 S.W.3d 233, 240-42, 2014 WL 2932282 at **6-8 (Ark.2014). The Arkansas court held that a defendant whose jury checked the Option D checked by Dansby’s jury, despite the presentation of mitigating evidence, see id. at **5, had “not demonstrated that error occurred at his trial with respect to the jury’s completion of the special-verdict forms on mitigating evidence.” Id. at **11.
B.
Also after this case was first briefed and argued, Dansby applied for an expanded certificate with respect to Claim V, his argument that ineffective assistance of trial counsel violated his rights under the Sixth Amendment. The district court dismissed the claim as procedurally defaulted because Dansby did not present the alleged deficiencies in counsel’s performance to the Arkansas courts. Dansby contends that the intervening decision of the Supreme Court in Maples v. Thomas, — U.S.-, 132 S.Ct. 912, 181 L.Ed.2d 807 (2012), excused his default on that claim.
Maples held that a habeas petitioner showed cause that excused his procedural default under state law when the attorney representing the petitioner abandoned him without notice, and thereby occasioned the default. 132 S.Ct. at 922. In that circumstance, the attorney had severed the principal-agent relationship and no longer served as the client’s representative, so the *827attorney’s error was not attributable to the petitioner client. Id. at 923.
Dansby contends that his postconviction attorney, David Talley, ceased to act as his agent because he suffered from a conflict of interest. He highlights the Supreme Court’s favorable citation in Maples of Ja-mison v. Lockhart, 975 F.2d 1377, 1380 (8th Cir.1992), which held that attorney conduct may provide cause to excuse a state procedural default where, as a result of a conflict of interest, a postconviction attorney “ceased to be [the petitioner’s] agent.” See 132 S.Ct. at 923.
The factual basis for the assertion of a conflict of interest is as follows. At trial, Dansby was represented by attorney Jan Thornton. Another attorney, Didi Sailings, was then a staff attorney with the Arkansas Death Penalty Resource Center. According to her testimony at the postcon-viction hearing, Sailings was not counsel of record for Dansby, but she “helped on the Dansby case.” Postconviction R. 193. At the time of Dansby’s postconviction proceeding, Sailings was the executive director of the Arkansas Public Defender Commission.
When Dansby filed his petition for post-conviction relief in state court in May 1995, he was represented by attorney A1 Schay. In June 1995, Schay filed a motion for leave to file an expanded amended petition. As an attachment to that amended petition, Schay included an affidavit signed by Sailings. Sailings averred that she had been assigned, as an attorney with the Resource Center, to provide assistance to attorney Thornton in Dansby’s case. The Sailings affidavit listed multiple reasons why Sailings believed that Thornton provided ineffective assistance at trial.
In August 1998, the postconviction court appointed attorney Talley, public defender for Union County, Arkansas, to represent Dansby in postconvietion proceedings. Several months later, attorney Katherine Streett of the public defender’s office wrote to the judge to express her “concern” that attorneys employed by the Arkansas Public Defender Commission “may be unable to represent Mr. Dansby” due to a conflict. Streett recounted that Sailings was then the executive director of the commission and the “titular boss” of attorneys Streett and Talley. Streett’s letter expressed concern that because Sailings provided assistance to Thornton before and during Dansby’s trial, it appeared that the proceeding must address not only Thornton’s representation of Dansby, but also Sallings’s representation. Streett suggested that the situation created at least “the appearance of a conflict if a public defender represents Mr. Dansby.”
The record includes no response from the court and no motion of counsel to withdraw or motion to substitute counsel. Talley and Streett represented Dansby at the evidentiary hearing in the postconviction proceeding. Talley called Sailings as a witness. Consistent with her affidavit, Sailings testified to her belief that Thornton provided ineffective assistance.
We are not convinced there is a debatable question whether Talley ceased to be Dansby’s agent because of an alleged conflict of interest between Dansby and Sailings. Sailings was not counsel of record for Dansby at his trial. When Dansby filed his petition for postconviction relief, represented by an attorney unaffiliated with the public defender system, he elected to focus his claims of ineffective assistance of counsel on the performance of attorney Thornton. Sailings actually filed an affidavit in support of Dansby’s expanded petition, attacking the quality of Thornton’s representation. Sailings then testified at the postconviction hearing in support of Dansby’s contention that Thornton was ineffective.
*828In this federal habeas action, Dansby seeks to avoid the procedural default of his ineffective assistance claims in order to challenge Thornton’s performance at trial. Even if Dansby had wished to challenge the “assistance” provided by Sailings, moreover, there is no showing that Talley and Streett owed any duty of loyalty to Sailings as a result of her “titular” status as executive director of the public defender commission. There is also no claim that Sailings had any role in supervising the representation of Dansby in the postcon-viction proceeding. In our view, this case is a long way from the “veritable perfect storm of misfortune,” 132 S.Ct. at 929 (Alito, J., concurring), that befell the petitioner in Maples, who missed the filing deadline for a notice of appeal because he was left without any functioning attorney of record and had no reason to suspect that he had been reduced to pro se status.
Dansby also asserts that his agency relationship with postconviction counsel was severed because attorney Talley did not meet the qualifications required for appointment of counsel in capital postconviction proceedings in Arkansas. See Ark. R.Crim. P. 37.5 (1998). He first raised this point in the district court in a “Supplement to Motion To Alter or Amend Judgment Pursuant to Fed.R.Civ.P. 59(e).” R. Doc. 80.3 The district court denied this aspect of the motion to alter or amend on the ground that Dansby raised an argument that could have been and should have been raised previously. Because the issue was not raised properly in the district court, we will not expand the certificate of appealability to address it on appeal. Freeman v. Busch, 349 F.3d 582, 589 (8th Cir.2003).
IV.
After the Supreme Court’s remand, believing that “the issues presented were adequate to deserve encouragement to proceed further,” Slack, 529 U.S. at 484, 120 S.Ct. 1595 (internal quotation omitted), we expanded the certificate of appealability to include the claims that the district court ruled were procedurally defaulted— Claims IV, V, VIII, IX, X, XI, XII, XIII, XIV (in part), XV, XVII, XIX, XXIV, XXV, and XXVI. Dansby argues that none of these claims is defaulted, and alternatively that any default is excused under the equitable rule of Martinez v. Ryan, — U.S.-, 132 S.Ct. 1309, 182 L.Ed.2d 272 (2012), and Trevino, 133 S.Ct. 1911.
Coleman v. Thompson, 501 U.S. 722, 752-55, 111 S.Ct. 2546, 115 L.Ed.2d 640 (1991), established a rule that “ineffective assistance of counsel during state post-conviction proceedings cannot serve as cause to excuse factual or procedural default.” Wooten v. Norris, 578 F.3d 767, 778 (8th Cir.2009). Martinez announced a “narrow exception” to the Coleman rule:
Where, under state law, claims of ineffective assistance of trial counsel must be raised in an initial-review collateral proceeding, a procedural default will not bar a federal habeas court from hearing a substantial claim of ineffective assistance at trial if, in the initial-review collateral proceeding, there was no counsel or counsel in that proceeding was ineffective.
*829132 S.Ct. at 1320. The Court defined “initial-review collateral proceeding” as a collateral proceeding that provides the first occasion to raise a claim of ineffective assistance at trial. Id. at 1315. Martinez “addresse[d] only the constitutional claims presented in [that] case, where the State barred the defendant from raising the claims on direct appeal.” Id. at 1320.
In Trevino, however, the Supreme Court expanded that rule, holding that Martinez applies where the “state procedural framework, by reason of its design and operation, makes it highly unlikely in a typical case that a defendant will have a meaningful opportunity to raise a claim of ineffective assistance of trial counsel on direct appeal.” 133 S.Ct. at 1921. This court then held that Martinez and Trevino apply to cases arising from Arkansas. Sasser v. Hobbs, 735 F.3d 833, 853 (8th Cir.2013).
A.
Dansby argues that none of his claims is defaulted, so no exception to procedural default is required, because he can still exhaust the claims in Arkansas state court through motions to recall the mandate in the state supreme court. But Dansby did not raise this contention in the district court until his Rule 59(e) motion after the district court’s order denying his petition, so it is not properly before us on appeal. Freeman, 349 F.3d at 589.
In any event, a motion to recall the mandate is not a proper vehicle for exhausting state remedies in Arkansas. A petitioner must exhaust his claims in state court through a State’s established appellate review process. O’Sullivan, 526 U.S. at 844, 119 S.Ct. 1728. A motion to recall the mandate in Arkansas is not part of Arkansas’s standard review process; it is “extraordinary rather than routine.” Wooten, 578 F.3d at 784-86. Dansby argues that recent Arkansas decisions show that the motion to recall has become routine, because the Arkansas Supreme Court has granted three motions to recall the mandate since Wooten, and has considered but denied several more. In Wooten, this court ruled that despite recalls of the mandate in three capital cases over three years, the motion to recall remained “extraordinary rather than routine.” Id. at 783-84. That three more mandates have been recalled, and several others denied, in the last five years is not enough to warrant reconsidering our opinion in Wooten. Whatever claims Dansby failed to present to the state courts are now procedurally defaulted, because no standard review process exists for him to exhaust the claims in state court.
B.
Dansby also contends that even if no avenue to exhaust state remedies is available, the district court erred in concluding that two of his claims are procedurally defaulted. He objects to the district court’s sua sponte determination that Claim XXVI — asserting ineffective assistance of trial counsel during voir dire— was defaulted, and he argues that Claim X — based on Batson v. Kentucky, 476 U.S. 79, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986)-was fairly presented to the state courts.
1.
Claim XXVI of Dansby’s second amended petition asserts that his defense team “unreasonably and prejudicially failed to protect [his] constitutional rights to be convicted and sentenced by a fair and impartial jury.” R. Doe. 25-5, at 33. More specifically, the petition alleges that Dansby’s counsel failed to identify and excuse jurors who had exposure to pretrial media coverage, make appropriate objections and a record on a Batson claim, *830secure individualized voir dire, or ensure that his jury be drawn from a representative cross-section of the community.
The district court ruled that this claim was not presented during Dansby’s direct appeal or his petition for postconviction relief, and was therefore defaulted. We conclude, however, that Dansby raised this claim in his petition for postconviction relief, which argued that trial counsel “[tjotally failed to conduct voir dire examination appropriate to death penalty litigation.” Supp.App. 11. He also advanced the claim in his postconviction brief on appeal, which included a separate argument point that “the court erred in not finding appellant’s trial counsel to be ineffective in conducting voir dire.” Add. Dl. The claim is thus not defaulted, but we proceed to consider whether the district court’s dismissal may be affirmed on the alternative ground that the claim is without merit. See Fields v. Gibson, 277 F.3d 1203, 1217-18 (10th Cir.2002).
The state postconviction court ruled that “the record adequately illustrates that Thornton functioned effectively during voir dire.” Supp.App. 126. The court found that Thornton asked jurors about their exposure to pretrial publicity and whether it would affect them. At the state postcon-viction hearing, Thornton testified that she had prepared for voir dire and had taken advice from her advisor Sailings on some of the questions to ask. The postconviction court found “completely unsupported by the record” Dansby’s argument that Thornton “failed to preserve the argument that blacks were underrepresented on the panel and that they were improperly excluded in violation of Batson,” because Thornton objected on both grounds during voir dire. Supp.App. 122-23. The court also concluded that Dansby was not prejudiced by any deficiencies of trial counsel under the standard of Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), because the evidence against him “was substantial, and it could even be described as overwhelming.” Supp.App. 135. On appeal, the Arkansas Supreme Court rejected the argument “that Thornton was ineffective in conducting voir dire,” concluding that Dansby suffered no prejudice because he was not forced to exhaust all twelve of his peremptory challenges. Dansby, 84 S.W.3d at 861.
A writ of habeas corpus may not be granted unless the adjudication of the claim in state court proceedings resulted in a decision that was “contrary to, or involved an unreasonable application of, clearly established Federal law.” 28 U.S.C. § 2254(d)(1). Both state courts correctly stated the Strickland standard, and there is no contrary Supreme Court decision with materially indistinguishable facts, so the decision was not contrary to clearly established law.
To determine whether the decision involved an unreasonable application of clearly established federal law, we review the decision reached in state court proceedings, but not the quality of the reasoning process. Williams v. Roper, 695 F.3d 825, 833-37 (8th Cir.2012), cert. denied, — U.S. -, 134 S.Ct. 85, 187 L.Ed.2d 65 (2013). Whether or not the state supreme court was correct to rely on the number of peremptory challenges exercised, the state court decision denying relief was not an unreasonable application of Strickland. Dansby does not assert that a particular juror was biased or otherwise illustrate why the alleged deficiencies of trial counsel during voir dire resulted in prejudice. The state postconviction court reasonably concluded that the strength of the evidence against Dansby defeated his claim of prejudice arising from jury selection. The postconviction court also rea*831sonably determined that Thornton acted within the wide range of reasonable professional assistance by questioning jurors about pretrial publicity and preserving objections based on Batson. For these reasons, we conclude that Claim XXVI fails on the merits.
2.
Dansby next argues that the district court erred in determining that Dansby proeedurally defaulted his claim under Batson. The district court ruled that Dansby failed to present the Batson claim to the state courts on direct appellate review and, alternatively, that the claim was decided on the independent and adequate state ground that Dansby failed at trial to preserve the issue for review. Dansby contends that he fairly presented this argument to the Arkansas Supreme Court on direct appeal, and we agree. In his briefs to the state supreme court, Dansby cited Batson and excerpted the trial transcript of his Batson objection to the strike of a black juror. R. Doc. 17, at 6; R. Doc. 57-6. The State addressed the Batson claim in its opposition brief to the supreme court, R. Doc. 17-1, at 4-6, further evidencing his fair presentment of the claim. Jones v. Sussex I State Prison, 591 F.3d 707, 714 (4th Cir.2010). The state supreme court rejected a separate claim about a “defective jury panel” on the ground that it was not sufficiently developed at trial, 893 S.W.2d at 336, but the court did not hold that Dansby failed to preserve the Batson claim for review. We therefore conclude that the Batson claim was not defaulted, but we consider alternatively whether the district court’s dismissal may be affirmed on the merits. See Fields, 277 F.3d at 1217-18.
Dansby’s claim is based on the following colloquy during voir dire, when prosecuting attorney Wynne questioned a prospective black juror named Williamson about her ability to consider the death penalty:
MR. WYNNE: And Ms. Williamson, I’ll ask you the same question. Could you consider imposition of the death penalty in a matter such as this?
MS. WILLIAMSON: I’ll consider it but I don’t think it will be my first consideration.
MR. WYNNE: If the defendant is found guilty of capital murder then you have two choices.
MS. WILLIAMSON: Yeah, I can consider it.
MR. WYNNE: And can you consider both choices, that is life in prison without parole or imposition of the death penalty?
MS. WILLIAMSON: Right. Yes, I can.
MR. WYNNE: Okay, could you kind of tell me what you meant when you said that, and I don’t mean to be picking on you, but you said that wouldn’t be your first choice.
MS. WILLIAMSON: Well, what I’m saying is I’m not for it and I’m not against it. But if it come [sic] down to, you know, life imprisonment, I would choose life before death. It just depends. I’m not really for the death penalty.
MR. WYNNE: But you said you were kind of — you said you’re not really for the death penalty.
MS. WILLIAMSON: I’m not comfortable with it. But yes, I can consider it. I can — I’m not comfortable with it.
MR. WYNNE: Do you have religious or philosophical or just personal problems with it? I mean, what — is it religion?
MS. WILLIAMSON: No.
*832MR. WYNNE: Just kind of personal, you just—
MS. WILLIAMSON: Yes. But I can consider the death penalty.
T. Tr. 175-77.
The State moved to excuse the juror. Dansby’s counsel raised a Batson objection and asked that the prosecution give a reason for striking the juror. The prosecutor responded that the juror appeared to be frustrated by questions about the death penalty, said she was not for the death penalty, and seemed hesitant about it. The trial court found that the State had given a race-neutral reason for the strike that was “sufficient,” and overruled the objection. T. Tr. 184.
On direct appeal, the Arkansas Supreme Court affirmed Dansby’s conviction without discussing the Batson claim. Dansby assumes that the Arkansas Supreme Court did not adjudicate his claim on the merits and urges this court to remand for the district court to review the claim de novo. But “[w]hen a federal claim has been presented to a state court and the state court has denied relief, it may be presumed that the state court adjudicated the claim on the merits in the absence of any indication or state-law procedural principles to the contrary.” Harrington v. Richter, 562 U.S. 86, 131 S.Ct. 770, 784-85, 178 L.Ed.2d 624 (2011). This presumption applies “when a state-court opinion addresses some but not all of a defendant’s claims.” Johnson v. Williams, — U.S. -, 133 S.Ct. 1088, 1094, 185 L.Ed.2d 105 (2013). “When a state court rejects a federal claim without expressly addressing that claim, a federal habeas court must presume that the federal claim was adjudicated on the merits — but that presumption can in some limited circumstances be rebutted.” Id. at 1096.
Dansby does not rebut the presumption that his Batson claim was adjudicated on the merits; he observes only that the Arkansas Supreme Court did not address his claim. Dansby himself points out that the Arkansas Supreme Court has “long held ... that when life is at stake, [the court] will make [its] own examination of the record and reject or accept on their merits all objections made at trial, whether or not argued on appeal.” Fretwell v. State, 289 Ark. 91, 708 S.W.2d 630, 634 (1986). Fret-well fortifies the presumption of Richter and Johnson v. Williams that the state court adjudicated Dansby’s Batson claim on the merits.
Because Dansby’s claim was adjudicated on the merits, our review is governed by 28 U.S.C. § 2254. We must determine what arguments or theories could have supported the state court’s decision, and then ask “whether it is possible fair-minded jurists could disagree that those arguments or theories are inconsistent with the holding in a prior decision of [the Supreme] Court.” Richter, 131 S.Ct. at 786. Batson calls for the trial court to determine whether the defendant has made a prima facie showing that the prosecutor exercised a peremptory challenge based on race. 476 U.S. at 96-97, 106 S.Ct. 1712. If the showing is made, then the burden shifts to the prosecution to present a race-neutral explanation for striking the juror. Id. at 97-98, 106 S.Ct. 1712. The defendant ultimately bears the burden of establishing that the prosecution engaged in purposeful discrimination. Id. at 98,106 S.Ct. 1712.
The state trial court implicitly found that Dansby made a prima facie showing, and called for an explanation by the prosecution. The trial court then found that the reason given by the prosecutor was race-neutral and that it was “sufficient.” We must give a presumption of correctness to the trial court’s finding of no purposeful *833discrimination. Smulls v. Roper, 535 F.3d 853, 861-62 (8th Cir.2008)(en banc). On appeal, the state supreme court reasonably could have upheld the trial court’s finding of no purposeful discrimination, given Juror Williamson’s expressed hesitancy about the death penalty. See Strong v. Roper, 737 F.3d 506, 511-12 (8th Cir.2013). Accordingly, we affirm the dismissal of Claim X on the alternative ground that it lacks merit.
C.
The remaining claims in the expanded certificate of appealability can be organized into three groups: (1) claims of ineffective assistance of trial counsel, numbered IV, V, and XV, (2) a claim of ineffective assistance of direct appeal counsel, numbered XIX, and (3) claims of error at trial, which the parties call “gateway” claims, numbered VIII, IX, XI, XII, XIII, XIV (insofar as the district court found it defaulted), XVII, XXIV, and XXV.
Martinez and Trevino addressed the first category — claims of ineffective assistance of trial counsel. As to the second and third categories, therefore, we must consider whether the equitable exception to procedural default recognized in those eases should be extended to claims of ineffective assistance of direct appeal counsel and claims of error at trial.
Most circuits to address the point have declined to extend Martinez to claims alleging ineffective appellate counsel, and we agree. Martinez focused on a “claim of ineffective assistance at trial,” 132 S.Ct. at 1315, emphasizing that the Sixth Amendment right to trial counsel “is a bedrock principle in our justice system” and “the foundation for our adversary system.” Id. at 1317; see also Trevino, 133 S.Ct. at 1921. The right to appellate counsel has a different origin in the Due Process Clause, see Evitts v. Lucey, 469 U.S. 387, 396-97, 105 S.Ct. 830, 83 L.Ed.2d 821 (1985), and even “the right of appeal itself is of relatively recent origin,” Martinez v. Ct. of App. of Calif., 528 U.S. 152, 159-60, 120 S.Ct. 684, 145 L.Ed.2d 597 (2000), so a claim for equitable relief in that context is less compelling. Most important, in announcing the equitable exception in Martinez for claims of ineffective assistance of counsel at trial, the Court was clear that the “rule of Coleman” — that ineffective assistance of counsel during state postcon-viction proceedings cannot serve as cause to excuse procedural default — “governs in all but the limited circumstances recognized here.” 132 S.Ct. at 1320. Those limited circumstances involved a claim that trial counsel was constitutionally ineffective. We therefore decline to extend Martinez to claims alleging ineffective assistance of counsel on direct appeal. Accord Reed v. Stephens, 739 F.3d 753, 778 n. 16 (5th Cir.2014); Hodges v. Colson, 727 F.3d 517, 531 (6th Cir.2013); Banks v. Workman, 692 F.3d 1133, 1148 (10th Cir.2012). But see Ha Van Nguyen v. Curry, 736 F.3d 1287, 1293-94 (9th Cir.2013). The district court properly dismissed Claim XIX.
The case for extending the equitable exception of Martinez to claims of trial error is likewise unconvincing. Dansby contends that once a petitioner shows that trial counsel was ineffective, the court should recognize an equitable exception to procedural default that allows him to advance claims of trial error that his ineffective trial counsel failed to preserve. “The problem with this line of argument is that there is no logical necessity to expand Martinez from the ineffectiveness claim itself to the underlying claims.... [A]s a practical matter, a petitioner in federal habeas needs only one winning claim to gain relief — if he’s got a winning ineffectiveness claim he doesn’t need another.” 7 *834Wayne R. LaFave et al., Criminal Procedure § 28.4(d) (3d ed.). We agree with the foregoing analysis and decline to extend Martinez to claims of trial error. The district court properly dismissed Claims VIII, IX, XI, XII, XIII, XIV, XVII, XXIV, and XXV.
The remaining claims, numbered IV, V, and XV, involve alleged ineffective assistance of trial counsel. In light of Trevino and Sasser, the equitable exception to procedural default applies to these claims if Dansby meets the criteria established in Martinez. A federal court is allowed to find “cause,” thereby excusing a habeas petitioner’s procedural default in Arkansas, where (1) the claim of ineffective assistance of trial counsel was a “substantial” claim; (2) the “cause” consisted of there being “no counsel” or only “ineffective” counsel during the state collateral review proceeding; and (3) the state collateral review proceeding was the “initial” review proceeding with respect to the “ineffective-assistance-of-trial-counsel claim.” Trevino, 133 S.Ct. at 1918. A “substantial” ineffective-assistance claim is one that has some merit. Martinez, 132 S.Ct. at 1318.
Dansby contends that he need not show a “substantial” ineffective-assistance claim at this juncture, because this court’s decision in Sasser automatically requires a remand for the district court to consider his claims. In Sasser, however, this court affirmed without remand the dismissal of twelve ineffective-assistance claims as “procedurally barred, meritless, or both.” 735 F.3d at 850. Four claims were deemed “potentially meritorious” and remanded for an evidentiary hearing. Id. at 851. Sasser thus does not establish an automatic remand rule; it stands instead as authority that this court may evaluate whether claims of ineffective-assistance are “substantial” or “potentially meritorious” in the course of determining whether a remand is warranted.
The State argues that none of Dansby’s claims qualify for the equitable exception of Martinez, because his postconviction counsel was not ineffective, and because none of the present claims raises a substantial issue under the Sixth Amendment that Dansby received ineffective assistance from trial counsel. We consider first the substantiality of Dansby’s present claims alleging ineffective assistance of trial counsel, and conclude that none of them warrants an equitable ruling to excuse Dans-by’s procedural default.
Claim V. In Claim V of his second amended petition, Dansby alleges eight instances of ineffective assistance during the guilt phase of his trial. The five sub-claims that were procedurally defaulted are not substantial. The other three sub-claims were resolved in state court, so they are not defaulted, and no certificate of appealability should have been granted as to those sub-claims.
First, Dansby argues that Thornton was ineffective for failing to present the affirmative defense of self-defense. Dansby contends that Thornton should have taken advantage of evidence that Kimble arguably fired a gun at Dansby, and evidence that Dansby and Brenda struggled over a firearm outside the house before Brenda was shot. Thornton’s strategy instead was to question the State’s evidence on premeditation, which was a necessary predicate to a conviction for capital murder. Sailings testified during post-conviction proceedings that self-defense “was not going to be a defense,” and that she “[did]n’t think we could have gone with a straight self-defense.” Supp.App. 206.
Dansby does not make a substantial case that Thornton performed defi-ciently by pursuing the chosen strategy. *835Under Arkansas law, “[djeadly physical force is justified as self-defense only if the use of such force cannot be avoided as by retreating.” Girtman v. State, 285 Ark. 18, 684 S.W.2d 806, 807 (1985); see also Ark.Code § 5-2-607. Evidence at trial showed that Dansby initiated the encounter on the day of the shooting by traveling to Brenda’s home while carrying a firearm. Brenda was shot and killed with her own gun, thus making it very difficult for Dans-by to convince a jury that force could not be avoided by retreating from the unarmed ex-wife. The medical examiner noted that Kimble had six gunshot wounds, including two in the back. Dansby, 893 S.W.2d at 335. Justin testified that he watched his father kick Kimble several times after he had finished shooting him. Id. at 334. Faced with this evidence, it was not unreasonable for Thornton to conclude that pure self-defense was unlikely to be a successful strategy, and to focus instead on convincing the jury that Dans-by’s acts were not premeditated. For similar reasons, there is no substantial case of prejudice arising from counsel’s decision not to pursue a theory of self-defense.
Second, Dansby claims that Thornton failed adequately to impeach McDuffie on cross examination, including with questions about a twenty-dollar payment from El Dorado police, a prior inconsistent statement to police about the timing of Dansby’s admissions, the nature of McDuffie’s prior relationship with Dansby, and McDuffie’s history of dishonesty or criminal convictions. Thornton did impeach McDuffie on some points, and how much to impeach a witness is generally a matter of trial strategy left to the discretion of counsel. United States v. Orr, 636 F.3d 944, 952 (8th Cir.2011). But even if Thornton was ineffective for not locating additional impeachment evidence and questioning McDuffie in all the ways that Dansby now identifies, we conclude that there is no substantial claim of prejudice. There was strong evidence to support the jury’s finding of guilt without reliance on McDuffie’s testimony, see ante, at 816-17, and additional impeachment of McDuffie likely would not have made a difference in the outcome.
Third, Dansby asserts that Thornton was ineffective for failing to call an expert witness to “educate jurors” about the reliability of child witnesses to undermine the force of testimony from Dansby’s son, Justin. This claim does not qualify for an equitable exception to procedural default because there is not a substantial showing of prejudice. Thornton cross-examined Justin, bringing out inconsistencies in his story and demonstrating his confusion for the jury. She highlighted the ways in which Justin’s story had changed: he initially told police that Dansby shot Kimble before Brenda, but at trial testified that his mother was shot first. Thornton’s cross-examination of Justin also showed that he was confused on other points and that he made contradictory statements about where he had been during the shootings. Based on Thornton’s cross-examination and on common knowledge about youth, a reasonable juror would have understood that there were reasons to question Justin’s reliability without the need for an expert to say so. Viewing Justin’s testimony in context of the entire record, there is no reasonable probability that an expert on child testimony would have altered the outcome.
Fourth, Dansby says that Thornton was ineffective for failing to object to the prosecutor’s “besmirchment” of her character during closing argument. At trial, Thornton called Jeffrey Talley as a defense witness. Talley had been a cellmate of McDuffie and Dansby during the entire time the two were housed together. *836He testified that Dansby had told him and McDuffie about the shooting, and that Dansby said he shot only after Kimble tried to shoot him first. Talley was also represented by Thornton. During argument, the prosecutor suggested that the jury should “think, long and hard,” about the credibility of Talley, “who just happens to have the same counsel as Mr. Dansby.” T. Tr. 646.
Whether to object during opposing counsel’s summation to the jury is a matter of trial strategy, and Thornton testified during state postconviction proceedings that she opted not to object too much for fear the jury would think “that you have something to hide.” Supp.App. 186. The prosecutor’s comments make up only eight lines of his closing argument, so it was understandable that Thornton would not emphasize the comments further by objecting to them. Strategic decisions like this one are “virtually unchallengeable,” Link v. Luebbers, 469 F.3d 1197, 1204 (8th Cir.2006), and we see no substantial argument that Thornton’s decision was outside the wide range of reasonable professional assistance.
Fifth, Dansby complains that Thornton was ineffective for failing to object to testimony of police officers about Dansby’s silence. As discussed earlier, ante, at 819-20, federal law was not clearly established on the permissibility of this testimony, and the state courts reasonably could have viewed the testimony as an explanation of the circumstances of Dans-by’s interview, not as a penalty for invoking the right to remain silent. “A failure to raise arguments that require the resolution of unsettled legal questions generally does not render a lawyer’s services outside the wide range of professionally competent assistance sufficient to satisfy the Sixth Amendment.” Hamberg v. United States, 675 F.3d 1170, 1173 (8th Cir.2012) (internal quotations and alteration omitted). There also is no likely prejudice based on the failure to object, given the reasonable view of the state courts that the testimony was permissible.
Finally, Dansby advances two sub-claims of ineffective assistance that were raised during Dansby’s state postconviction proceedings: that counsel failed to request a change of venue in light of extensive media coverage and failed to object to testimony describing the deaths of Brenda and Kim-ble as “murders.” Supp.App. 129, 54, 133-36. These sub-claims were thus not defaulted by postconviction counsel, and Martinez does not apply. The certificate of appealability improvidently encompassed these sub-claims, and we revoke the certificate insofar as it covered sub-claims that were not procedurally defaulted. As to the rest of the sub-claims, the district court properly dismissed Claim V notwithstanding Martinez and Trevino.
Claim IV. In Claim IV of the second amended petition, Dansby alleges that three separate conflicts of interest adversely affected the performance of trial counsel Thornton. The first asserted conflict is that Thornton’s husband previously represented Brenda Dansby, allegedly in relation to her problems with Dansby. Dansby also asserts that George Taylor, who worked part-time as a public defender in the office where Thornton worked, represented McDuffie for a time. Third, Dansby claims that another part-time public defender, Jack Barker, after initially being appointed by a state court to represent Dansby in the murder case, represented McDuffie on unrelated criminal charges and advised him on cooperating with law enforcement on Dansby’s case. Dansby does not allege that the part-time defenders undertook these representations on behalf of the public defender’s office.
*837In cases involving an attorney’s concurrent representation of defendants with conflicting interests, the Supreme Court has held that “a defendant who shows that a conflict of interest actually affected the adequacy of his representation need not demonstrate prejudice in order to obtain relief.” Cuyler v. Sullivan, 446 U.S. 335, 349-50, 100 S.Ct. 1708, 64 L.Ed.2d 333 (1980). But it is an “open question” in the Supreme Court whether the Sullivan rule applies to cases of “successive representation.” Mickens v. Taylor, 535 U.S. 162, 176, 122 S.Ct. 1237, 152 L.Ed.2d 291 (2002). This court has found “much to be said in favor of holding that [Sullivan’s ] rationale favoring the ‘almost per se rule of prejudice’ does not apply outside the context of a conflict between co-defendants or serial defendants.” Caban v. United States, 281 F.3d 778, 782 (8th Cir.2002). Other conflict situations, we explained, “may have such limited consequences that they will not invariably demonstrate prejudice,” and “sound reasoning supports requiring a defendant to prove actual prejudice under the Strickland standard in order to meet the constitutional standard for ineffective assistance of counsel.” Id.; see United States v. Young, 315 F.3d 911, 914 n. 5 (8th Cir. 2003) (“[Wjhere the alleged conflict involves ethical issues other than multiple or serial representation, this Circuit has held that Strickland is still the appropriate standard.”) (citing Caban, 281 F.3d at 783-84). We find no authority that a part-time public defender’s representation of a client in private practice is imputed to another public defender. But even if the representations by Taylor and Barker (or even Thornton’s husband) were imputed to Thornton, there was no concurrent representation of codefendants while Thornton represented Dansby, and no serial representation of codefendants. In light of Caban, therefore, we conclude that Dansby does not raise a substantial claim based on Sullivan.
When the Sullivan presumption does not apply, Dansby must show that his trial counsel performed deficiently and that he was prejudiced by counsel’s inadequate performance. Strickland, 466 U.S. at 687, 104 S.Ct. 2052. We see no substantial Sixth Amendment claim on either prong. Dansby asserts that the alleged conflicts of interest caused Thornton to refrain from investigating Brenda’s life, presenting a self-defense theory, or aggressively cross-examining McDuffie. We discern no substantial reason to believe that Thornton withheld the provision of a vigorous defense to Dansby because of work performed previously by her husband, Taylor, or Barker.
Even if the representations by Taylor and Barker must be imputed to Thornton, moreover, Dansby has not presented a substantial claim that the outcome would have been different. As discussed above, there was no prejudice from the alleged failures to present a self-defense theory or to cross-examine McDuffie more extensively. If the prior representation of Brenda by Thornton’s husband deterred Thornton from casting her in a negative light, Dans-by points to nothing about Brenda’s life that might have been exploited by the defense to overcome the substantial evidence of Dansby’s guilt.
For these reasons, we conclude that Dansby has not shown that Claim IV presents a substantial claim of ineffective assistance of trial counsel that would justify an equitable exception to procedural default, even assuming that Dansby’s postconviction counsel was ineffective. The district court properly dismissed Claim TV.
Claim XV. In Claim XV, Dansby raises five sub-claims that trial counsel was ineffective during the penalty phase of his *838trial. We conclude that none of those sub-claims is substantial enough to warrant an equitable exception to procedural default. Another sub-claim was presented in state postconviction proceedings and is therefore not proeedurally defaulted. The cer-tifícate of appealability is revoked as to that issue.
First, Dansby claims that trial counsel was ineffective for not investigating his early life. He explains that most of his siblings were born of his mother’s extramarital affairs. He alleges that both of his parents grew up in difficult homes, and that their marriage—before they separated when Dansby was fourteen years old— was characterized by arguments and physical altercations in front of Dansby and his siblings. Most of the proffered evidence relates not to Dansby’s life, but to the lives of his parents. It is not the kind of “powerful” undeveloped evidence that might establish a reasonable probability of a different sentence. See Wiggins v. Smith, 539 U.S. 510, 534-36, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003). There is not a substantial claim of prejudice.
Second, Dansby alleges that Thornton should have prepared a “complete social history” and provided it to a psychologist, so that the psychologist could have testified about the effect of Dansby’s upbringing on his relationship with Brenda. Specifically, Dansby claims that a psychologist would have told the jury that his childhood was “virtually tailor-made” to create attachment problems and insecurity, and that an unstable relationship exacerbates such psychological issues. Dansby believes that the psychologist would have explained why Dansby’s relationship with Brenda was “so tumultuous and why it had persisted for so long,” and that the testimony would have “humanized” Dansby. R. Doc. 25-4, at 16-21.
Trial counsel did call a psychologist in the penalty phase. The psychologist testified that the relationship between Dansby and Brenda was the type “that keeps people on edge, that keeps them under stress.” He said that the couple’s on-again/off-again relationship was difficult for Dansby and “played a big role in forming his behavior.” T. Tr. 730-31. This evidence is substantially similar to that which he now says Thornton should have offered: it sought to explain why Dansby’s relationship with Brenda was volatile and could have had the same “humanizing” effect. We see no substantial argument of prejudice based on counsel’s failure to offer functionally similar expert testimony that purportedly would have identified another reason for the difficult relationship.
Third, Dansby contends that trial counsel was ineffective for failing to challenge the State’s portrayal of him as a “habitual wife beater and stalker.” Dans-by says counsel should have presented evidence of the “ongoing relationship” between Dansby and Brenda, and testimony from other women with whom Dansby had been involved. R. Doc. 25-4, at 21-22. Trial counsel did present several witnesses who testified about the ongoing relationship between Dansby and Brenda. There is no reasonable probability that more evidence about the ongoing relationship would have made a difference to the outcome.
Dansby’s contention that trial counsel should have called ex-girlfriends as witnesses is not substantial. Dansby asserts that the witnesses would have testified that Dansby was not violent during his intimate relationships with them. Then, Dansby says, the psychological expert would have testified that the “differences in the attachment styles” of women explain why Dansby’s relationship with Brenda “so badly triggered [Dansby’s] attachment dif-*839Acuities in a way that relationships with other women did not.” R. Doc. 25-4, at 22. It is speculative whether a strategy focused on Brenda’s “attachment style,” which could well be construed by a jury as an effort to “blame the victim,” would have produced a different outcome. This claim of ineffective assistance is not substantial.
Fourth, Dansby claims that trial counsel ineffectively failed to object to a lack of evidence to support the three aggravating circumstances found by the jury. The jury found that Dansby previously committed a violent felony, that he knowingly created a great risk of death to a person other than the victim during the commission of capital murder, and that he committed the capital murder in an especially cruel or depraved manner. Trial counsel did object on sufficiency grounds to the “especially cruel or depraved manner” circumstance, so Dansby’s allegation on that point is unsupported. Counsel also objected to the “risk of death to a person other than the victim” circumstance, albeit on other grounds, but the trial court then determined that the evidence was sufficient to submit the circumstance, so a more specific objection would not have affected the outcome.
In support of the circumstance that Dansby previously committed a violent felony, the State offered proof of Dansby’s prior conviction for false imprisonment. Dansby argues that trial counsel should have sought an instruction on the elements of false imprisonment, so the jury could have been persuaded that the crime is not a violent felony. It was not unreasonable for counsel to withhold objection, and Dansby suffered no prejudice, because Dansby’s prior conviction plainly qualified. The final jury instruction required proof beyond a reasonable doubt that “Dansby previously committed another felony an element of which was the use or threat of violence to another person or creating a substantial risk of death or serious physical injury to another person.” T. Tr. 777-79; see Ark.Code § 5-4-604(3). Dansby pleaded guilty to false imprisonment in the first degree in Arkansas, a felony offense that occurs where, “without consent and without lawful authority, the person knowingly restrains another person so as to interfere substantially with the other person’s liberty in a manner that exposes the other person to a substantial risk of serious physical injury.” Ark.Code § 5 — 11— 103(a) (emphasis added); see id. § 5 — 11— 103(b). The State presented a record of Dansby’s conviction and thereby proved that he was convicted of the qualifying offense. See Collins v. State, 338 Ark. 1, 991 S.W.2d 541, 545-46 (1999).
Fifth, Dansby complains that trial counsel failed to rebut evidence of Dans-by’s false imprisonment of Brenda. He says that several witnesses could have testified that Brenda and Dansby were seen together during the time of captivity, that Brenda was “relaxed and happy, enjoying a wine cooler and talking excitedly” about a shopping trip, and that there was no indication she was forced to do anything against her will. This testimony, however, would not have rebutted the testimony of three prosecution witnesses who recounted an earlier portion of the episode. These witnesses testified that as Brenda attempted to run into her sister’s home, Dansby held a gun to her head, dragged her by her hair, and forced her into his car before driving away. Evidence of Brenda’s demeanor at a later time would not have rebutted the prosecution’s evidence describing how she came to be falsely imprisoned, and it would not have undermined the fact of Dansby’s conviction. We therefore conclude that there is no substantial claim that Dansby was prejudiced by counsel’s failure to offer the proffered evidence.
*840Sixth, Dansby argues that trial counsel should have located witnesses to testify about his “psychosocial history,” “life history,” and his “functioning” around the time of the murders. R. Doc. 25-4, at 9-10. Dansby similarly argued in state post-conviction proceedings that trial counsel was ineffective in failing properly to prepare the penalty phase of his trial, and in failing to call certain witnesses. The Supreme Court of Arkansas rejected this claim, observing that “[t]he decision to call a particular witness is one of strategy,” and that “[t]rial counsel must use his or her best judgment to determine which witnesses will be beneficial to his client.” Dansby, 84 S.W.3d at 862. The court also explained that Dansby failed “to demonstrate what other witnesses Thornton should have called and what their testimonies would have been.” Id. Dansby’s present claim about additional witnesses suffers from the same shortcoming and is materially indistinguishable from the claim resolved by the state supreme court. Our expansion of the certificate of appealability was designed to permit further exploration of the application of Martinez and Trevino to claims that Dansby defaulted in state proceedings. Claims relating to the calling of witnesses that were resolved in the state court proceedings are not procedurally defaulted, so we withdraw the certificate with respect to those claims.
For these reasons, we conclude that Dansby has not alleged a substantial claim of ineffective assistance of counsel at the penalty phase that warrants an equitable exception to the rule of procedural default, even assuming that postconviction counsel was ineffective. The district court properly dismissed Claim XV.4
D.
Aside from his reliance on Martinez and Trevino, Dansby argues that the district court should have convened an evidentiary hearing to consider whether his asserted actual innocence should provide a “gateway” to avoid procedural default and to allow consideration of his defaulted claims on the merits. See Schlup v. Delo, 513 U.S. 298, 115 S.Ct. 851, 130 L.Ed.2d 808 (1995). We concluded above, in Section II.A, that Dansby’s evidence is insufficient to meet the high standard that would be required to support a freestanding claim of actual innocence. Although the standard of proof for a “gateway” claim of actual innocence is slightly lower, Dansby still must “demonstrate that more likely than not, in light of the new evidence, no reasonable juror would find him guilty beyond a reasonable doubt.” House v. Bell, 547 U.S. 518, 538, 126 S.Ct. 2064, 165 L.Ed.2d 1 (2006). This standard “is demanding and permits review only in the ‘extraordinary’ case.” Id. (quotation omitted). For *841essentially the same reasons that Dansby cannot meet the Herrera standard for a freestanding claim of actual innocence, he is not entitled to a hearing on his claim of actual innocence under Schlup.
For the foregoing reasons, we vacate the dismissal of Claim II and Claim III in Dansby’s second amended petition and remand the case for further consideration of those claims. We affirm the dismissal of the remaining claims on appeal.
. In Clayton v. Roper, 515 F.3d 784 (8th Cir. 2008), a panel of this court said that because the habeas petitioner could not point to an independent constitutional violation in his state criminal proceeding, the federal court was "without jurisdiction” to consider his claim of actual innocence. We are unsure why the Clayton panel thought it lacked jurisdiction, so we follow the approach of Herrera, 506 U.S. at 417-19, 113 S.Ct. 853, in addressing Dansby’s claim.
. It is unnecessary to consider the district court’s alternative ruling that any Doyle error was harmless, but we note that Hill’s disputed answer is cumulative of Officer Stegall’s testimony earlier in the trial that Dansby “invoked his rights and stated that he didn't want to say anything else without a lawyer.” Trial R. 676.
. Dansby has not challenged the qualifications of attorney Schay, who filed the petition that identified Dansby’s claims for postconviction relief. Cf. Ark. R.Crim. P. 37.5 (1998) (providing that “[a]t least one of the attorneys " appointed to represent the postconviction applicant shall have certain qualifications) (emphasis added). The record does not reflect whether Schay withdrew from representing Dansby in the state postconviction proceeding after Talley was appointed. The district court appointed Schay to represent Dansby in the federal habeas proceeding. R. Doc. 4.
. Dansby argues that by granting a certificate of appealability to consider his claims of ineffective assistance of trial counsel, this court necessarily concluded that the claims are "substantial.” When a claim is dismissed based on procedural default, a certificate should be granted only where there is a debatable constitutional claim and a debatable procedural ruling. Slack, 529 U.S. at 484, 120 S.Ct. 1595. Because Martinez compared the determination whether an ineffective-assistance claim is "substantial” to the standards for issuance of certificates of appeala-bility, 132 S.Ct. at 1318-19, Dansby asserts that the issuance of a COA must mean that the constitutional claim is substantial.
Dansby’s contention that the COA resolved the issue of procedural default strikes us as inconsistent with his proffered supplemental brief in support of an expanded COA, which sought a "plenary appeal” to consider "the merits of Mr. Dansby’s claims and procedural arguments.” But if Dansby is correct in his current position, then our conclusion that certain ineffective-assistance claims are not "substantial” may be construed as the revocation of the COA as to those claims.