What is our role in reviewing a sentence imposed by the federal district court?

Discussion. When we review a sentence imposed by the district court, our role is not to "substitute [our] judgment for that of the sentencing court as to the appropriateness of a particular sentence; rather, in applying the Eighth Amendment, [we] decide[ ] only whether the sentence under review is within constitutional limits." United States v. Valdez, 16 F.3d 1324, 1334 (2d Cir.) (quoting Solem v. Helm, 463 U.S. 277, 290 n. 16 (1983)), cert. denied, 115 S.Ct. 60 (1994). Consequently, "successful challenges to the constitutionality of particular sentences are extremely rare." Id.