I know, the covered ones are great!
My pair have had one since they were little, although I had taken the door off cos it was too heavy for them! Lol
Now that they are bigger and I've moved the litter box into the bathroom I put the door back on and they'r fine... Exept from when Maisy's pooing and Milo will sometimes go and smack her with the door- on purpose!! Cheeky bugger. Lol