Try using a small sandbox, that might have higher sides. I use the really large litter pans. I used to use the covered pans, but some of my fluffier cats don't seem comfortable in them, they can't turn around well enough.

My girl Allie digs and digs and digs, and it is just for fun. So, I don't always think it is for some strange reason. I also keep a piece of carpet under the boxes. So, any extra litter just gets cleaned up, and I don't stress as much...