More height (8"+) is desirable for rats, because the adults have a long reach when they stand up, AND because when they get bored, they'll be chewing on the top if they can easily reach it. Not so much if it's awkwardly higher over their heads.It sounds as if you're planning to build these cages? Keep in mind that they need to easily reach the over-head food hopper, IF you're incorporating that design. (& I recommend it- it's the only way to keep their food clean & with less waste.)