We have a covered litter box too. The cats didn't like it covered at first.

Our Jackson sticks his head out while he goes, but I don't think he makes faces while doing his business.

For Rosie, she goes into the box head first.

The litter box is plastic, and Twidgit sounds like she is scratching a hole in the side, she actually scratches the litter very little.

I think its Ashton that sometimes does not cover his deposits at all.