For wrapping up wounds, both large and small, you want a wrap that is secure, yet not so tight it will decrease needed blood circulation. Ace bandages are considered too constricting and likely to wind up tight; in their stead pros use conforming bandages, with brands names like Kling. The key here is “wider is better.” Get the widest width you can and wrap liberally. The bandage will cling to itself (you still have to tape the end of it) but will not shift around much in normal use. The same stuff as Kling, but about 10 times cheaper is Vet-Wrap, used for the same purposes on animals. Better yet, Vet-Wrap comes in a choice of cheery colors instead of hospital white.