SUTTON, Circuit Judge. When Ricardo Woods shot David Chandler in the head, he might have thought that he had silenced him for good. But while paralyzed from the neck down, Chandler retained some movement in his eyelids. In the days before he succumbed to his injuries, Chandler used a system of blinks to identify his assailant. At Woods’ murder trial, the court allowed the State to introduce Chandler’s identification of Woods, holding it an admissible dying declaration. An Ohio jury convicted him, and the state courts affirmed the decision. Woods filed a habeas petition alleging a violation of his Confrontation Clause rights under the Sixth (and Fourteenth) Amendment. He also claimed the court misapplied Batson by not timely requiring the State to offer a race-neutral explanation for a peremptory strike. Because neither of these claims satisfies the strictures of review under AEDPA, we affirm their rejection.