All of mine love the covered litter boxes and Vixen wants a spotless litterbox each time she uses. So if the all the covered ones happen to have something in them and the only spotless one is the open one she complains. She refusing to use the open ones unless she simply cannot wait for one of the others to be cleaned to her satisfaction. (Usually this means 1 poopoo or 1 peepee.) She is a super fussy one.

My covered box are large boxes. Meant for multi cats. They use the 2 large ones before the smaller ones.