Since most tubs in racks are no more than about 6" I guess that would be the minimum height that you'd need. I have an RBI cage that's 14" tall and that much height is really a waste of space to be honest. My BP doesn't do anything besides hide in one of his two hides. I even have an area in the middle of the cage with wood that has some height to it, but he never uses it. The only time he gets vertical is at night and he's really just looking for a way out.