I always had a hard time finding a litter box that was deep enough for my cats. They kicked loads of litter out the side with traditional boxes. Then I tried a covered box and it just made them stinky when they came out. So I made my own litter box.
I simply bought two deep Rubbermaid containers (I think Rubbermaid would be better than Sterilite since Rubbermaid is a little more flexible) and cut two openings in the front of the containers. I had my dad actually cut the openings with a saw, but I think a sharp box cutter (and a little safety precaution) would work, too. This has been the "perfect" solution for my cats because they only spill litter out the front, and even then it's not very much.