  The binding energies of deformed even-even nuclei have been analysed within
the framework of a recently proposed microscopic-macroscopic model. We have
used the semiclassical Wigner - Kirkwood $\hbar$ expansion up to fourth -
order, instead of the usual Strutinsky averaging scheme, to compute the shells
corrections in a deformed Woods - Saxon potential including the spin-orbit
contribution. For a large set of 561 even-even nuclei with $Z\ge 8$ and $N\ge
8$, we find an {\it rms} deviation from the experiment of 610 keV in binding
energies, comparable to the one found for the same set of nuclei using the FRDM
of M\"oller and Nix (656 keV). As applications of our model, we explore its
predictive power near the proton and neutron drip lines as well as in the
superheavy mass region. Next, we systematically explore the fourth - order
Wigner - Kirkwood corrections to the smooth part of the energy. It is found
that the ratio of the fourth - order to the second - order corrections behaves
in a very regular manner as a function of the asymmetry parameter $I=(N-Z)/A$.
This allows to absorb the fourth - order corrections into the second - order
contributions to the binding energy, which enables to simplify and speed up the
calculation of deformed nuclei.
