Defendant-Appellant Martin Alvarado-Gonzalez (Alvarado) appeals the 41-month sentence imposed following his plea of guilty to being an alien unlawfully present in the United States following deportation for an aggravated felony. He contends that his 16-level increase for a prior aggravated felony and his resultant sentence were unreasonable in light of the factors set forth in 18 U.S.C. § 3553(a).

Alvarado’s sentence was within a properly calculated advisory guideline range and is presumed reasonable. See United States v. Alonzo, 435 F.3d 551, 554 (5th Cir. 2006). Such a sentence is given “great deference,” and we infer that the sentencing court considered all the factors for a fair sentence under § 3553(a). See United States v. Mares, 402 F.3d 511, 519-20 (5th Cir.), cert. denied, — U.S.-, 126 S.Ct. 43, 163 L.Ed.2d 76 (2005). We conclude that Alvarado has failed to rebut the presumption that his sentence, which was at the bottom of the applicable range under the Sentencing Guidelines, was reasonable. See United States v. Smith, 440 F.3d 704, 707 (5th Cir. 2006).

Alvarado challenges 8 U.S.C. § 1326(b)’s treatment of prior felony and aggravated felony convictions as sentencing factors rather than elements of the offense in light of Apprendi v. New Jersey, 530 U.S. 466, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000). Alvarado’s constitutional challenge is foreclosed by Almendarez-Torres v. United States, 523 U.S. 224, 235, 118 S.Ct. 1219, 140 L.Ed.2d 350 (1998). Although Alvarado contends that Almendarez-Torres was incorrectly decided and that a majority of the Supreme Court would overrule Almendarez-Torres in light of Apprendi, we have repeatedly rejected such arguments on the basis that Almendarez-Torres remains binding. See United States v. Garza-Lopez, 410 F.3d 268, 276 (5th Cir.), cert. denied, — U.S. -, 126 S.Ct. 298, 163 L.Ed.2d 260 (2005). Alvarado properly concedes that his argument is foreclosed in light of Al *343 mendarez-Torres and circuit precedent, but he raises it here to preserve it for further review.

AFFIRMED.