United States v. Jackson, 559 F.3d 368 (5th Cir. 2009)
When an initial term of supervised released is revoked, the district court may impose a new term of supervised release as part of a revocation sentence.

The maximum length of this new term is calculated as follows: “The length of such a term of supervised release shall not exceed the term of supervised release authorized by statute for the offense that resulted in the original term of supervised release, less any term of imprisonment that was imposed upon revocation of supervised release. Jackson also notes that a district court may impose any term of supervised release that is equal to or greater than the mandatory minimum, less any term of imprisonment that was imposed upon revocation of supervised release.

United States v. Miller, 634 F.3d 841 (5th Cir. 2011)
The district court may not consider the factors listed 18 U.S.C. 3553(a)(2)(A), which include “the seriousness of the offense, to promote respect for the law, and to provide just punishment for the offense,” when modifying or revoking a term of supervised release.

United States v. Tapia, 131 S. Ct. 2382 (2011)
Section 3582(a) does not permit a sentencing court to impose or lengthen a prison term in order to foster a defendant’s rehabilitation.