We previously remanded this habeas matter to the district court for an evidentiary hearing on whether the petitioner is mentally retarded and, thus, ineligible for the death penalty, a sentence of the Texas state court.1 After conducting a hearing, the federal district court found that Hall was not retarded. Reasonable jurists would not disagree with the careful analysis of the district court or that the issues presented were inadequate to deserve encouragement to proceed further.2
Hall also seeks a certificate of appealability (COA) on two other issues: whether the Texas death penalty statute or the mitigation special issue submitted to the *747jury violates the Constitution. Ultimately, Hall has failed to make a substantial showing of the denial of a constitutional right— for essentially the reasons stated by the district court.3
We deny each of Hall’s requests for a COA.
. See generally Hall v. Quarterman, 534 F.3d 365 (5th Cir.2008).
. See Miller-El v. Cockrell, 537 U.S. 322, 336, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003). We note that the district court on remand — despite Hall's claim that it should not have— properly gave deference to the state court's determinations of factual issues. See 28 U.S.C. § 2254(e)(1) ("[A] determination of a factual issue made by a State court shall be presumed to be correct. The applicant shall have the burden of rebutting the presumption of correctness by clear and convincing evidence.”).
. See Hall v. Quarterman, 443 F.Supp.2d 815 (N.D.Tex.2006), vacated on other grounds by Hall v. Quarterman, 534 F.3d 365 (5th Cir.2008).