  We consider type II string theory compactified on a symmetric T^6/Z_2
orientifold. We study a general class of discrete deformations of the resulting
four-dimensional supergravity theory, including gaugings arising from geometric
and "nongeometric'' fluxes, as well as the usual R-R and NS-NS fluxes. Solving
the equations of motion associated with the resulting N = 1 superpotential, we
find parametrically controllable infinite families of supersymmetric vacua with
all moduli stabilized. We also describe some aspects of the distribution of
generic solutions to the SUSY equations of motion for this model, and note in
particular the existence of an apparently infinite number of solutions in a
finite range of the parameter space of the four-dimensional effective theory.
