One of our kitties, I had to raise from about 2 weeks in age, and I was amazed at how neat/clean it was to just go through the feed - groom- cleanup cycle. Even though she obviously was not litter-trained at such a young age, she only eliminated during the groom/cleanup task. So there never was any mess in her little bed!
She grew up to be a robustly healthy (though small), clever tortie, and is now eight years old.