Be sure to know the 8-movers good, and then look at every case and find out how to make them an 8-mover, but cancel one move. It's easier when you notice thazt they're always 3-gen.
Also, aside from the A perm A9, each setup breaks the "adjacent non-interchangeable" pair, and by breaking it, it allows the moved corner to be interchangeable with the other corners after both a single and quarter turn.
ie R'U2R'D2RU2R'D2R2, R turns break UBR and BUL, R' makes it interchangeable with BUL and R2 makes it interchangeable with DBL.