No, I don't recommend a covered box. You may need to change litters to see which one he prefers. Keep putting him in the litter box and train him that way. Is he constipated? That might explain the vocalization during elimination. He may need some mineral oil in his food to help lubricate things.
Sometimes, adding another litter pan may help.
Dr. Lou
Edited by dr4pets on September 6 2006 at 5:47 PM
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Dr. Louis Gotthelf
Animal Hospital of Montgomery
Pet Skin and Ear Clinic