  The formation of supershells observed in large metal clusters can be
qualitatively understood from a periodic-orbit-expansion for a spherical
cavity. To describe the changes in the supershell structure for different
materials, one has, however, to go beyond that simple model. We show how
periodic-orbit-expansions for realistic cluster potentials can be derived by
expanding only the classical radial action around the limiting case of a
spherical potential well. We give analytical results for the leptodermous
expansion of Woods-Saxon potentials and show that it describes the shift of the
supershells as the surface of a cluster potential gets softer. As a byproduct
of our work, we find that the electronic shell and supershell structure is not
affected by a lattice contraction, which might be present in small clusters.
