To answer all of the questions posed by your responses.
- both boys are neutered
- none of my cat boxes are covered
- Max never bothers Felix when he's in the box
- the stools are pretty firm and dry and always have been for both cats, so I guess my next step would be a trip to the vet (you know they love that)
- I keep several litter boxes, but I'm not particularly diligent about cleaning (I change the litter once each week)

I have decided to try switching to the clumping litter and see if that helps, just in case it's the smell of the urine in the box that may be causing him to go outside the box.

Felix is a great cat and this is his only problem, so whether or not I resolve this he will stay with me in my home for the rest of his life - I'll just clean up after him if I have to.

Thanks again to all.