X and Y are Banach spaces for which K(X, Y), the space of compact operators from X to Y, is an M-ideal in L(X, Y), the space of bounded linear operators form X to Y. If Z is a closed subspace of Y such that L(X, Z) has property SU in L(X, Y) and d(T, K(X, Z)) = d(T, K(X, Y)) for all $T in L(X, Z)$, then K(X, Z) is an M-ideal in L(X, Z) if and only if it has property SU is L(X, Z).