Melvin Velez-Santos pleaded guilty to, and was convicted of, one count of conspiracy to commit offenses against the United States, see 18 U.S.C. § 371, and two counts of making a false statement to a federally licensed firearm dealer, see 18 U.S.C. §§ 922(a)(6), 924. The district court sentenced him to 240 months in prison, and Velez-Santos timely filed a notice of appeal. His lawyer later filed a motion to dismiss the appeal with prejudice, which we granted.

Velez-Santos then filed a 28 U.S.C. § 2255 motion to vacate, set aside, or correct his prison sentence, contending that his lawyer was unconstitutionally ineffective because he filed a motion to dismiss the appeal without authorization from Velez-Santos. The district court held an evi-dentiary hearing, at which Velez-Santos and his lawyer testified. The court found that the lawyer “testified quite clearly that ... he did have [Velez-Santos’] authority to dismiss the appeal prior to filing of the motion with the Eleventh Circuit.” Crediting the lawyer’s testimony, the court found that Velez-Santos was “in agreement to dismiss his appeal,” and it denied the § 2255 motion. The court, however, granted a certificate of appealability on the following issue: “[W]hether appellate counsel rendered ineffective assistance of counsel by moving to dismiss [Velez-Santos’] direct criminal appeal without the authorization of [Velez-Santos].”

We review as a mixed question of law and fact the district court’s denial of a § 2255 motion. So we review only for clear error the court’s factfindings, but we review de novo the court’s application of the law to those facts. McKay v. United States, 657 F.3d 1190, 1195 (11th Cir. 2011). *811 A district court’s factfindings are “clearly erroneous only if the record lacks substantial evidence to support [them].” Johnson v. Hamrick, 296 F.3d 1065, 1074 (11th Cir. 2002) (quotation marks omitted).

Substantial evidence supports the district court’s finding that Velez-Santos’ lawyer had authorization from Velez-Santos to file the motion to dismiss the appeal. The lawyer testified that he had that authorization, and the court credited the lawyer’s testimony. We give substantial deference to that credibility determination. See Crystal Entm’t & Filmworks, Inc. v. Jurado, 643 F.3d 1313, 1322 (11th Cir. 2011). Also, Velez-Santos did not respond to a letter from this Court asking him if he had any objections to the motion to dismiss the appeal, even though he testified that he had received that letter. Because Velez-Santos’ § 2255 motion is based on his lawyer not having authorization to file the motion to dismiss the appeal, and because the district court found that the lawyer did have that authorization, the court did not err in dismissing the § 2255 motion.

AFFIRMED.