There are only seven possible orientations for the corners (plus one solved). Since we can ignore edges (there are none), we can use a few algs that are shorter than usual.

Name Diagram Algorithm Comments Video
U F (R U R' U') F' This is just the easy T orientation, also known as "Edges Bar."
T (R U R' U') (R' F R F') This is the other T-orientation.
L F (R U') (R' U' R U) (R' F') This is the orientation that makes up the first half of the Y-perm.
S (R U R' U) (R U2 R') This is just the standard Sune.
As (R U2 R' U') (R U' R') This is the Antisune.
Pi F (R U R' U') (R U R' U') F' For this one, I just do one of the "L" orientations. It's just F (R U R' U')*2 F'.
H R2 U2 R U2 R2 This is a special 2x2 algorithm that only requires 5 moves, so it's pretty nice.