  We study the phenomenology of a class of models describing modular invariant
gaugino condensation in the hidden sector of a low-energy effective theory
derived from the heterotic string. Placing simple demands on the resulting
observable sector - such as proper electroweak symmetry-breaking, superpartner
spectra consistent with current limits and neutralino relic densities of an
acceptable magnitude - results in significant restrictions on the possible
configurations of the hidden sector.
