Great diaper cover with one flaw

The Rumparooz newborn diaper covers are a great fit on our tall and skinny 8 day old girl. We are using them over fitted cloth diapers from a diaper service.
However, the tag and area with the company logo allow weeping of wetness into clothes which means a very small area on her back seems to always get wet and we have to change her sleepers often which is not the best situation.