TMOY
Veteran
If you use alternatively the Y-perm and its inverse (which is also a Y-perm but rotates centers in the opposite direction), you can even use it whenever you have no corner parity. Unfortunately you have no way to fix that parity without affecting centers at all, you must either keep track of what you're doing to centers or solve them before the parity fix...Don't feel so bad, infact the bolded words relate exactly to me, I found out about this a week or so ago and have still only had 3 successes. Luckily though I didn't dedicate to much solves with corners before centers. Remember you can still do corners first if the swaps are divisible by 4, which is quite often.