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.

Name	Diagram	Algorithm	Comments
T		(R U R' U') (R' F) (R2 U') (R' U' R U) (R' F')	I use the T-perm 3x3 alg. You could alternatively use the J-perm or A-perm alg.
T		x2 (R U R' U') (R' F) (R2 U') (R' U' R U) (R' F')	Just rotate to put the solved layer on the bottom and do a Y-permutation.
Y		(F R U') (R' U' R U) (R' F') (R U R' U') (R' F R F')	I use the Y-perm 3x3 alg. You could alternatively use the N-perm alg.
Y		z2y (F R U') (R' U' R U) (R' F') (R U R' U') (R' F R F')	Just rotate to put the solved layer on the bottom and do a Y-permutation.
UF/DF		(R2 U' R2') (U2' y) (R2 U' R2')	Rotate in the direction of y as you perform the U2'.
U adj D diag		(R U' R) F2 (R' U R')	If you have D2 of this case, you can mirror it.
U diag D adj		(L D' L) F2 (L' D L')	If you have U2 of this case, you can mirror it. You could also perform z2 and do the alg above.
UD diag		R2 F2 R2	Rejoice. This is the nicest case.