Corner orientation is done in two steps. If the sum of the orientations of the top corners is divisible by 3, use the U/D cases to solves the top and bottom. If not, use a U case, which will change the orientation of one corner in the D layer, and fix the orientation of the U layer corners. Then a normal alg from the seven can be used for the D layer, you just have to remember the orientation from the three other corners and remember what they match up with. Technically, this method has no setup moves. But you can find out how that works yourself :)
Rotate U and D layers so they match the pictures before executing any algs. If you do not, you may mess up your D layer and execute the wrong alg. If you already know how to orientate the 'normal' corner orientations, there is only 16 algs to learn. If you don't, there are 23. If you have any questions, comments, corrections or any money you want to give me, just email. 







U R L' D' R2 U2 R' D R2 U2 L U' L2 B2 L2 
x2 z (R U R' U R U2 R' L' U' L U' L' U2 L) z’ x2 
R U R' U R U2 R' L' U' L U' L' U2 L 
U' B U' F U2 B2 D' R2 U D F' U' B 
U R' U L U' D' F2 D R2 U2 L' U R' 
B R U R' U R U2 R' L' U' L U' L' U2 L B' 
U F U R' D' L F2 L' F D R F2 U2 F' U2 F 
F2 L F2 L' U2 R U' R' F2 R' F2 R U' 
U R' F2 R F2 R U R' U2 L F2 L' F2 
U F2 U' R2 D2 L D' R D' R D' L' D 
U F2 U' D' L D R' D R' D L' D2 R2 
U2 R L F' L' B L' B L' F L2 B2 R' 
R' D L' D L' D R U' D' F2 U L2 D2 
R2 U2 L2 D B' D' L2 D' F' D F U2 R2 F' 
U F2 R2 U' L' U L B2 L D L' B2 R2 F2 
U R2 U B U' R2 D2 L2 F L2 D2 F' U' F 
R' U2 R' B' R U2 L2 D2 F' D2 L2 F R F' 
U' R U L2 B2 U' B2 L2 F2 R D' R' F2 R' 
U2 F2 D2 B L' B' D2 B' R' B R F2 U2 R' 
U R' D2 L U L' U' L D2 R' D B2 D L2 D2 R2 
R2 D2 L2 D' B2 D' R D2 L' U L U' L' D2 R U' 
U R U' R' U L2 D' L B2 L U2 L2 D2 R D' L2 
U R2 L D2 L' U B' U2 L U D2 R2 U' L F' L2 
You only need to look at three corners, the orientation of the fourth is already fixed. But make sure the layer is rotated so the red X would be in the top left, as this is the corner affected by the top layer. These can be learnt by intuition, but I've put them here for completeness sake. In the table, there are multiple situations that are the same. They are left in because I am too lazy to take them out, and it gives you a wider option of choices.
Turn over the cube to execute these algs. Solved! (When you see three correct corners in the bottom layer, just put the wrong one at the topleft.) 



























