BTW, the litter box I've used for YEARS now, and totally LOVE, is the Omega Paw self-cleaning litter box. It's covered, and what you do to clean it is simply roll it over on its top (it has a rounded top), kinda tap the bottom with your hand to dislodge any wet litter, tip it back to normal position, and voila! All the dirty litter and crap is in a little drawer that you pull out and dump. Then you can fill the little drawer with clean litter and scatter it back on top. The drawer stays in the box. You don't have to touch a scoop or dig through it or anything.
The cats seem to like using it (as long as I stay on top of keeping it clean!), and since for the reasons I mentioned in my housekeeping thread the litter box has to be in the living room for now, it is much less yucky than having an open box. I use one for my two adult cats and it is fine for them.
The other great invention I discovered is the "litter locker." It's a small plastic gadget that you put a roll of liners in. Each time you empty the drawer from the litter box into the litter locker, you give the litter locker handle a turn, and the litter is locked in. When it gets too full to turn, you open the litter locker and remove the plastic containing the dirty litter and easily throw it in the trash.
I get totally skeeved having to handle litter, so this is the best solution I have found. Minimal contact, minimal mess, cats like it.