  We present a complete and systematic analysis of the Minkowski extrema of the
N=1, D=4 Supergravity potential obtained from type II orientifold models that
are T-duality invariant, in the presence of generalised fluxes. Based on our
previous work on algebras spanned by fluxes, and the so-called no-go theorems
on the existence of Minkowski and/or de Sitter vacua, we perform a partly
analytic, partly numerical analysis of the promising cases previously hinted.
We find that the models contain Minkowski extrema with one tachyonic direction.
Moreover, those models defined by the Supergravity algebra so(3,1)^2 also
contain Minkowski/de Sitter minima that are totally stable. All Minkowski
solutions, stable or not, interpolate between points in parameter space where
one or several of the moduli go to either zero or infinity, the so-called
singular points. We finally reinterpret our results in the language of type IIA
flux models, in order to show explicitly the contribution of the different
sources of potential energy to the extrema found. In particular, the cases of
totally stable Minkowski/de Sitter vacua require of the presence of
non-geometric fluxes.
