In what circumstances will a sentencing judge impose a non-Guidelines sentence or Guidelines sentence?

In the wake of United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), which ruled that the Guidelines are advisory, a sentencing judge may impose either a Guidelines sentence or a non-Guidelines sentence. See, e.g., id. at 245-46, 125 S.Ct. 738; United States v. Crosby, 397 F.3d 103, 113 (2d Cir.2005) ("Crosby"). In arriving at either type of sentence, the sentencing judge must consider the factors set forth in 18 U.S.C. 3553(a). That section provides in pertinent part as follows: