  A ring is called $n$-perfect ($n\geq 0$), if every flat module has projective
dimension less or equal than $n$. In this paper, we show that the
$n$-perfectness relate, via homological approach, some homological dimension of
rings. We study $n$-perfectness in some known ring constructions. Finally,
several examples of $n$-perfect rings satisfying special conditions are given.
