Brandon J. Smith pleaded guilty to an indictment charging him for being a felon in possession of a firearm and was sentenced to a 41-month term of imprisonment and to a three-year period of supervised release. The district court overruled Smith’s objection to the probation officer’s recommendation that an adjustment in offense level for acceptance of responsibility be denied because Smith had denied falsely the offense conduct.

To obtain a two-level reduction for acceptance of responsibility, a defendant must clearly demonstrate acceptance of responsibility for his offense. U.S.S.G. § 3El.l(a); United States v. Lghodaro, 967 F.2d 1028, 1031 (5th Cir. 1992). The defendant must truthfully admit the conduct comprising the offense of conviction. See U.S.S.G. § 3E1.1, comment. (n.l(a)). This court reviews a district court’s finding on acceptance of responsibility “under a standard of review even more deferential than a pure clearly erroneous standard.” United States v. Gonzales, 19 F.3d 982, 983 (5th Cir. 1994) (internal citation and quotation omitted).

Smith argues that he admitted his involvement in the offense at the change-of-plea hearing and at the sentencing hearing and that the district court gave too much weight to Smith’s false statements during his interview with the probation officer. *408 Smith contends that he was merely exercising his constitutional right against self-incrimination and that he should not be punished because he believed naively that he could still proceed to trial after pleading guilty.

The adjustment for acceptance of responsibility is in the nature of a reward, not a punishment, and does not unduly burden constitutional privileges. See United States v. Mourning, 914 F.2d 699, 707 (5th Cir. 1990). The district court did not clearly err in giving weight to the false statements made by Smith to the probation officer. Under the deferential standard applicable to the district court’s ruling, there is no basis for reversal. The judgment is AFFIRMED.