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.