For orientation of the LL corners there are eight configurations (one solved), these are
U, T, L, S, -S, H and pi
The oriented case I would like to call the O case (as in Olle, Olle is a Swedish nickname for Olof (Olaf, Olav), "hey, you got a Olle!", compare "Sune", "Nicklas"... that also are Swedish names (named by Lars Petrus). PLL is "Pelle", that is a nickname for "Per", more fun, in Sweden, in short storys about two random boys they most often are named "Olle" and "Pelle" =).
Well, the same configurations occure for CLL and COLL but there permutation also counts. Now if we look at the cases we see that, if the permutation is not correct two corners needs to swap. These corners are on one side of the last layer (if you place two corners correctly first).
The case where permutation is correct I like to call U, the diagonal D and for the rest R, F, L and B depending on wich side the swap is.
Here are the T cases as example, from left to right TU, TD, TF, TB, TL and TR
(images from Speedcubing.com)
But if this shall work then alignment of the U layer must be decided. The T, U, H and pi cases are pretty obvious but for S, -S and L there are a varaity of aligments used, we need a convention I think. For L I think it's also obvious, one unoriented sticker at uRf and one at ulB makes it look like a "L". Then to make a Sune look like a "S" we place one of the tree unoriented at uRb, one at urF an the last one at uLf and I think it looks a little like a "S", mirror: uRf, ulF, uLb for -S. (I know pictures would be great but I have no drawing tool installed, crashed this computer totaly a while ago and then, when restoring I did only install the stuff I need to surf)
All cases possible are:
TU, TD, TR, TL, TF, TB
UU, UD, UR, UL, UF, UB
LU, LD, LR, LL, LF, LB
SU, SD, SR, SL, SF, SB
-SU, -SD, -SR, -SL, -SF, -SB
PiU, PiD, PiR, PiL, PiF, PiB
HU, HD, HR/HL, HF/HB (HR + HL and HF + HB are the same cases)
OU, OD, OR/OL/OF/OB (corners oriented = permutation only needed. the last four are the same, OU is the solved case)
How about that?
Then we can use "hey! I found a great alg for the CLL-HD case" and such
He, just noted that the "SU" case is solved using the original "Sune" =P