In the first part of this paper, we give necessary and sufficient conditions for a quasi-projective module whose endomorphism ring has the powersubstitution property, by way of completion of diagrams. In the second part, we study exchange rings with the right power-substitution property. We prove that for any module M with the finite exchange property, the ring EndRR(M) has the right power-substitution property if (and only if) M has the power cancellation property, if and only if for any regular element , there exists an integer such that aIn is unit-regular in