When I was in college and still living with my parents, we had a cat with a low tolerance for dirty litter. if we didn't clean up her poop right away she'd poop in the bathtub! I can't tell you how many mornings I'd make my way to the shower in a stupor only to pull aside the shower curtain, turn on the water, and step in a pile of cat poo.
I use The World's Best Cat Litter (it's made from corn) and that seems to work well. It's made from corn and it lessens my concern about the cat ingesting it off of her paws or the dogs ingesting it if they get into her litter for a kitty treat.