As part of a project to derive parametric reduction schemes automatically a
systematic search has been set up to determine 'good sets of variables'. It
turns out that both the ease of derivation of a scheme and its efficiency
depend very sensitively on the choice of variables. For some topologies
there can be thousands of such choices. I report here on this search and
the resulting automatic derivations of practical schemes. As an example I
use four loop massless propagator topologies, but the results are
applicable for more complicated reactions with fewer loops as well.