  A consistent theoretical description of physics at high energies requires an
assessment of vacuum stability in either the Standard Model or any extension of
it. Especially supersymmetric extensions allow for several vacua and the choice
of the desired electroweak one gives strong constraints on the parameter space.
As the general parameter space in the Minimal Supersymmetric Standard Model is
huge, any severe constraint on it unrelated to direct phenomenological
observations enhances the predictability of the model. We perform an updated
analysis of possible charge and color breaking minima without relying on fixed
directions in field space that minimize certain terms in the potential (known
as "D-flat" directions). Concerning the cosmological stability of false vacua,
we argue that there are always directions in configuration space which lead to
very short-lived vacua and therefore such exclusions are strict. In addition to
existing strong constraints on the parameter space, we find even stronger
constraints extending the field space compared to previous analyses and combine
those constraints with predictions for the light CP-even Higgs mass in the
Minimal Supersymmetric Standard Model. Low masses for supersymmetric partners
are excluded from vacuum stability in combination with the 125 GeV Higgs and
the allowed parameter space opens at a few TeV.
