  We consider the two-dimensional N=(2,2) Wess-Zumino model with a cubic
superpotential at weak and intermediate couplings. Refined algorithms allow for
the extraction of reliable masses in a region where perturbation theory no
longer applies. We scrutinize the Nicolai improvement program which is supposed
to guarantee lattice supersymmetry and compare the results for ordinary and
non-standard Wilson fermions with those for SLAC derivatives. It turns out that
this improvement completely fails to enhance simulations for Wilson fermions
and only leads to better results for SLAC fermions. Furthermore, even without
improvement terms the models with all three fermion species reproduce the
correct values for the fermion masses in the continuum limit.
