  We discuss a procedure to simplify the Landau potential, based on Michel's
reduction to orbit space and Poincar\'e normalization procedure; and illustrate
it by concrete examples. The method makes use, as in Poincar\'e theory, of a
chain of near-identity coordinate transformations with homogeneous generating
functions; using Michel's insight, one can work in orbit space. It is shown
that it is possible to control the choice of generating functions so to obtain
a (in many cases, substantial) simplification of the Landau polynomial,
including a reduction of the parameters it depends on. Several examples are
considered in detail.
