Alonzo Lydell Burgess, an Alabama prisoner sentenced to death for murdering his girlfriend and two of her children, sought federal habeas relief under Atkins v. Virginia, which bars executing a person with intellectual disability. The state post-conviction court denied the claim without allowing the expert evaluation Burgess requested, and the Alabama Court of Criminal Appeals rejected it on the existing paper record. The federal district court likewise denied relief and refused an evidentiary hearing. The Eleventh Circuit reversed. Burgess had consistently sought funding and access for mental-health experts, but his state proceedings occurred before and shortly after Atkins, when the governing constitutional rule and Alabama’s substantive standard were still developing. The pre-Atkins record contained incomplete and conflicting evidence, including school history, prior IQ testing, and limited mental-health testimony; it did not reasonably support the state court’s conclusion. The panel held that the state determination was not entitled to AEDPA deference and that Burgess had been diligent in trying to develop the claim. Because a hearing could permit proof of facts entitling him to relief, the district court abused its discretion by denying one. The court vacated the federal judgment and remanded the entire case for further proceedings, leaving the ineffective-assistance claim unresolved.