Matrix-Element Corrections to Parton Shower Algorithms

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. LU TP 94-17 October 1994 Address after 1st January 1995: CERN TH Division, CH-1211 Geneva 23, Switzerland.