Nelson Castro Castillo appeals the below-guidelines sentence of 76 months of imprisonment imposed following his guilty plea conviction for illegal reentry by a previously deported alien after conviction of an aggravated felony. He argues the following. His sentence violates the Eighth Amendment because the 16-level enhancement that he received under U.S.S.G. § 2L1.2(b)(l)(A)(ii) was applied indiscriminately and was used to calculate both his offense level and criminal history category. He was inordinately punished based upon his prior conviction of an aggravated felony and the enhancement constitutes cruel and unusual punishment because it applies regardless of the facts underlying a defendant’s prior conviction. There is no empirical basis to justify treating all prior convictions for aggravated felonies the same under § 2L1.2 and his sentence is substantively unreasonable because a sentence that includes an enhancement under § 2L1.2 results from impermissible double counting and, therefore, is greater than necessary to meet the sentencing goals of 18 U.S.C. § 3553(a).

Our review is limited to plain error because Castro Castillo did not raise these arguments in the district court. See United States v. Neal, 578 F.3d 270, 272 (5th Cir. 2009). To prevail on plain error review, Castro Castillo must show a forfeited error that is clear or obvious and that affects his substantial rights. See Puckett v. United States, 556 U.S. 129, 135, 129 S.Ct. 1423, 173 L.Ed.2d 266 (2009). If he makes such a showing, we have the discretion to correct the error if it seriously affects the fairness, integrity, or public reputation of judicial proceedings. See id.

Castro Castillo’s assertion that his sentence violates the Eighth Amendment’s prohibition against cruel and unusual punishment is without merit. The Eighth Amendment prohibits a sentence that is greatly disproportionate to the offense because such sentences are “cruel and unusual.” McGruder v. Puckett, 954 F.2d 313, 315 (5th Cir. 1992). In deciding whether a sentence is unconstitutionally disproportionate, we make a threshold comparison between the gravity of the offense and the severity of the sentence. Id. at 315-16. In non-capital cases, successful challenges to the proportionality of sentences are “exceedingly rare.” Rummel v. Estelle, 445 U.S. 263, 272, 100 S.Ct. 1133, 63 L.Ed.2d 382 (1980).

The district court imposed a 76-month prison sentence that was within the statutory limits for the offense and that was below the properly calculated guidelines range, which is considered to be a “convincing objective indicator of proportionality.” 8 U.S.C. § 1326(b)(2); see United States v. Cardenas-Alvarez, 987 F.2d 1129, 1134 (5th Cir. 1993) (internal quotation marks and citation omitted). Castro Castillo has not otherwise established that his *387 sentence was grossly disproportionate to the severity of his offense of illegal reentry after an aggravated felony conviction. See Rummel, 445 U.S. at 265-66, 100 S.Ct. 1133. Thus, he has not demonstrated plain error in this regard. See Cardenas-Alvarez, 987 F.2d at 1134; Puckett, 556 U.S. at 135, 129 S.Ct. 1423.

His remaining challenges to the exces-siveness of his sentence are equally unavailing. The use of his prior conviction to calculate both his offense level and criminal history category was permissible, see United States v. Duarte, 569 F.3d 528, 529-30 (5th Cir. 2009), his sentence was not excessive, and he has failed to identify any precedent holding that the double counting of his prior conviction results in a sentence that violates the Eighth Amendment. See United States v. Evans, 587 F.3d 667, 671 (5th Cir. 2009). His claim that § 2L1.2 produces disproportionate sentences because it does not take into account the defendant’s prior conduct or the differences in severity among underlying prior convictions that trigger a 16-level enhancement lacks merit. See United States v. Rayo-Valdez, 302 F.3d 314, 317 (5th Cir. 2002); Cardenas-Alvarez, 987 F.2d at 1134. We have expressly rejected the argument that § 2L1.2’s alleged lack of an empirical basis renders unreasonable a sentence imposed under that Guideline and have indicated that courts need not examine the empirical grounding behind every Guideline. See Duarte, 569 F.3d at 529-31. Castro Castillo’s claim that his sentence is substantively unreasonable because it resulted from double-counting is, as he acknowledges, foreclosed by existing precedent. See id. at 529-30.

The judgment of the district court is AFFIRMED.