  The general constraints on the parameter space of soft-breaking terms, in
order to avoid dangerous charge and color breaking minima, are applied to the
four-dimensional string scenario where the dilaton is the source of
supersymmetry breaking (dilaton-dominated limit). The results indicate that the
whole parameter space is excluded on these grounds after imposing the present
experimental data on the top mass. The inclusion of a non-vanishing
cosmological constant does not improve essentially the prospects. Possible
way-outs to this situation are briefly discussed.
