  We consider flux compactifications of type IIB string theory on the mirror of
a rigid Calabi-Yau. In special cases, these models are dual to the type IIA
flux vacua with runaway direction in flux space. We show that new weak coupling
AdS solutions can be found for large complex structure, while Minkowski
solutions with all moduli stabilized are confined to be at strong coupling. The
existence of these solutions, as found in a previous work, is nevertheless
guaranteed by a non-renormalization theorem of the type IIB flux
superpotential. Based on our results, we are led to the conjecture that
supersymmetric runaway directions in flux space are always accompanied by a
spectrum of moduli masses reaching down to the AdS scale. This could be
violated in a non-supersymmetric situation.
