MEMORANDUM *
Steven Jaffe appeals the district court’s denial of his petition for writ of habeas corpus. He claims that the admission of a police officer’s preliminary hearing testimony at his trial violated his rights under the Confrontation Clause and the Due Process Clause of the Fourteenth Amendment. Jaffe also claims that his state-appointed trial counsel was ineffective in violation of the Sixth Amendment because he failed to object to the prosecutor’s misstatement of the law during the prosecutor’s rebuttal argument at Jaffe’s trial.
The district court rejected all of Jaffe’s claims and denied his habeas petition in full. We have jurisdiction under 28 U.S.C. § 2253(a). We affirm in part and reverse in part.
I.
We first address Jaffe’s Confrontation Clause claim. Jaffe argues that he did not have an adequate opportunity to cross-examine Officer David Miller at the preliminary hearing because Jaffe did not know at that time that Miller was under investigation on federal charges of official corruption. Thus, Jaffe claims, the admission of Miller’s preliminary hearing testimony at trial violated the Confrontation Clause.
While we are exceedingly troubled by Confrontation Clause implications that arise from the admission of Miller’s preliminary hearing testimony at trial, we cannot reach the merits of Jaffe’s.claim on this appeal. This is because Jaffe either has not exhausted or has procedurally defaulted on his Confrontation Clause claim in the state courts.
The rule requiring a habeas petitioner to exhaust all state-court remedies before seeking federal relief is codified at 28 U.S.C. § 2254(b)(1)(A). To satisfy the exhaustion requirement, a habeas petitioner must demonstrate either (1) that he has fairly presented his claim to the highest court with jurisdiction to consider it, or (2) that no state remedy remains available to him. See Johnson v. Zenon, 88 F.3d 828, 829 (9th Cir.1996).
Jaffe did not fairly present his Confrontation Clause claim to the state courts before raising that claim in his federal habeas corpus petition. In neither his direct nor his collateral appeals before the state courts did Jaffe make the argument that the state had violated his Confrontation Clause rights. We reject Jaffe’s contention that his Confrontation Clause claim was fairly presented for exhaustion purposes when he cited the Pennsylvania Supreme Court case Commonwealth v. Bazemore, 531 Pa. 582, 614 A.2d 684 (1992), in conjunction with the argument in his state briefing that the state had violated his due process rights under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). It is arguable whether Bazemore was decided on federal Confrontation Clause grounds, and in any event citation *559to that case as part of a due process argument and without mention of the word “confrontation” or anything similar could not have alerted the state courts that Jaffe was making a confrontation argument.
It is unclear from the record, however, whether any state remedies remain available for Jaffe to raise his Confrontation Clause claim. The district court did not address this issue, and the parties have not briefed it.1 Whether there remains a procedure in California that would enable Jaffe to raise his claim is important because if there is, the claim is unexhausted, but if there is not, the claim is likely procedurally barred. See Jennison v. Goldsmith, 940 F.2d 1308, 1312 (9th Cir. 1991), overruled on other grounds as recognized in Swoopes v. Sublett, 196 F.3d 1008, 1011 (9th Cir.1999). While the district court has discretion to permit a habeas petitioner to return to state court to present unexhausted claims, see King v. Ryan, 564 F.3d 1133, 1140-41 (9th Cir. 2009) (outlining both the “Kelly ” and the “Rhines ” procedures for curing “mixed” habeas petitions), it is required to dismiss with prejudice a claim that is procedurally defaulted under state law. See Coleman v. Thompson, 501 U.S. 722, 729-730, 111 S.Ct. 2546, 115 L.Ed.2d 640 (1991). Thus, while we hold that Jaffe has not fairly presented his Confrontation Clause claim to the state courts, we reverse the district court’s order on this claim and remand so that the court may determine in the first instance whether any California procedure remains available to Jaffe for raising that claim, in which case the district court can exercise its discretion to determine whether Jaffe’s petition should be stayed pursuant to either of the procedures outlined in King. See King, 564 F.3d at 1140-41.
II
Apart from his Confrontation Clause claim, Jaffe’s principal argument is that the state violated his due process rights under Brady when it failed to disclose information about the criminal investigation of Miller before Miller testified at Jaffe’s preliminary hearing. While there is some merit to Jaffe’s Brady argument, existing Supreme Court case law does not clearly establish that the prosecution was required to disclose the impeachment information about Miller before, rather than after, Jaffe’s preliminary hearing. Thus, the California courts’ decision to uphold Jaffe’s convictions over his Brady objection did not result from an “unreasonable application” of clearly established Supreme Court precedent, and we are constrained under the Antiterrorism and Effective Death Penalty Act (AEDPA) to leave that decision undisturbed. 28 U.S.C. § 2254(d).
We affirm the district court’s denial of Jaffe’s habeas petition as to his Brady claims.
III
Jaffe finally argues that his state-appointed trial counsel was ineffective in violation of the Sixth Amendment because he failed to object when the prosecutor misstated the law during his rebuttal argument. We affirm the district court’s holding that the California courts did not unreasonably apply Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), in rejecting Jaffe’s ineffective assistance of counsel claims.
Whether to enter formal objections during a prosecutor’s closing argu*560ments is a strategic decision that many trial counsel approach differently. Even if Jaffe’s counsel made a poor decision in not objecting to the prosecutor’s legal misrepresentation, it does not fall so short of the ordinary standards of the legal profession as to be objectively unreasonable within the meaning of Strickland. Moreover, it does not seem likely that Jaffe was prejudiced even if his counsel’s performance was deficient because both Jaffe’s defense counsel and the trial-court judge instructed the jury that operability was an element of the gun-related charges against Jaffe. It is impossible under these circumstances to say that the state courts’ application of Strickland was unreasonable for purposes of AEDPA. See Harrington v. Richter, — U.S. -, -, 181 S.Ct. 770, 788, 178 L.Ed.2d 624 (2011). The district court’s rejection of Jaffe’s ineffective assistance of counsel claim was accordingly proper.
Each party shall bear its own costs.
AFFIRMED IN PART, REVERSED IN PART, AND REMANDED.