  We constrain the parameter space of the minimal and gaugino-assisted anomaly
mediation, and gaugino mediation models by requiring that the electroweak
vacuum corresponds to the deepest minimum of the scalar potential. In the
framework of anomaly mediation models we find strong lower bounds on slepton
and squark masses. In the gaugino mediation models the mass spectrum is forced
to be at the TeV scale. We find extensive regions of the parameter space which
are ruled out, even at low tan(beta). The implications of these results on the
g-2 of the muon are also analyzed.
