  In the study of equisingularity of families of mappings Gaffney introduced
the crucial notion of excellent unfoldings. This definition essentially says
that the family can be stratified so that there are no strata of dimension 1
other than the parameter axis for the family. Consider a family of corank 1
multi-germs with source dimension less than target. In this paper it is shown
how image Milnor numbers can ensure some of the conditions involved in being
excellent. The methods used can also be successfully applied to cases where the
double point set is a curve. In order to prove the results the rational
cohomology description of the disentanglement of a corank 1 multi-germ is given
for the first time. Then, using a simple generalization of the Marar-Mond
Theorem on the multiple point space of such maps, this description is applied
to give conditions which imply the upper semi-continuity of the image Milnor
number. From this the main results follow.
