In alg.cubing.net, you can twist corners!
Here's the algorithm I used:
L' R' 4D R 4D' L 4B2 L' 4D R' 4D' L R D 4L F 4L' F' D' 4B2 D F 4L F' 4L' D'
This is possible because when you enter a move like "4D", it turns only the stickers of the U face, and not the pieces.
I'm interested in knowing...