LU TP 94-17 hep-ph/9410414 October 1994 Matrix-Element Corrections to Parton Shower Algorithms Michael H. Seymour We discuss two ways in which parton shower algorithms can be supplemented by matrix-element corrections to ensure the correct hard limit: by using complementary phase-space regions, or by modifying the shower itself. In the former case, existing algorithms are self- consistent only if the total correction is small. In the latter case, existing algorithms are never self-consistent, a problem that is particularly severe for angular-ordered parton shower algorithms. We show how to construct self-consistent algorithms in both cases.