  We derive stability conditions for the critical points of the no-scale scalar
potential governing the dynamics of the complex structure moduli and the
axio-dilaton in compactifications of type IIB string theory on Calabi-Yau
three-folds. We discuss a concrete example of a T^6 orientifold. We then
consider the four-dimensional theory obtained from compactifications of type
IIB string theory on non-geometric backgrounds which are mirror to rigid
Calabi-Yau manifolds and show that the complex structure moduli fields can be
stabilized in terms of H_{RR} only, i.e. with no need of orientifold
projection. The stabilization of all the fields at weak coupling, including the
axio-dilaton, may require to break supersymmetry in the presence of H_{NS} flux
or corrections to the scalar potential.
