Balance with flat objects

When computing derived functors of a functor of two variables there is often balance. This means that these functors can be computed using a resolution of either variable. Now that flat covers are known to exist in many categories, derived functors can be computed using flat resolutions. So it is natural to ask if we have balance in this situation. When the ring is left perfect we get the usual balance. This raises the question of whether these are the only rings where we get balance. In this article we show that if the ring R is commutative and noetherian, then R must be perfect in order to get the desired balance.