  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. The postscript file for this paper can also be obtained by
anonymous ftp from thep.lu.se in the file pub/Preprints/lu_tp_94_17.ps
