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 moduleMwith the finite exchange property, the ringEndRR(M) has the right power-substitution property if (and only if)Mhas the power cancellation property, if and only if for any regular element, there exists an integersuch thataInis unit-regular in