I started with a covered litter box and switched to uncovered. Cassy would sit on top of the box and terrorize his brother, Sassy, into staying inside (or outside) of it. He was getting very afraid of going in the box. Now, Livvy probably wouldn't put up with this behavior of Cassy's, but I'd gotten rid of the covered box by the time she entered our lives.

I think your cats must be more civilized than mine.