Before revision: Given a purely atomic probability measure with support on n points, P, any mean-preserving contraction  of P, Q, with support on m > n points is a mixture of mean-preserving contractions of P, each with support on most n points.
After revision: Given a purely atomic probability measure with support on n points, P, any mean-preserving contraction (mpc) of P, Q, with support on m > n points is a mixture of mean-preserving contractions of P, each with support on most n points.