I have trained our two cats to use one of those nesting-type cat pans. The top is a plastic mesh strong enough to hold the cat's weight, and the bottom is a container of the same plastic. Urine falls down through and solid stuff stays on top, where I can pick it up and flush it down the toilet. I do not use the liners sold by the company.

It took weeks of gradually decreasing the amount of litter (Feline Pine-like sawdust pellets) to fool the cats into doing without any litter at all, and things were very messy, as I had to scrub out the sawdust that caught in the mesh, but now I don't use any litter at all and am saving money and it's easy to clean out the pan, sterilize it with Chlorox, and so on. (After using Chlorox, I neutralize it, first rinsing with water, and then with a bit of a vinegar and water mix.)

I'm sure the cats would prefer to go back to the pellets, but they do use the new arrangement without "making mistakes," and things smell as good as they did with the pellets.

I keep the pan near the toilet, so it is easy to empty and rinse out.