  We provide a study of the phenomenology of heterotic orbifold
compactifications scenarii within the context of supergravity effective
theories. Our investigation focuses on those models where the soft Lagrangian
is dominated by loop contributions to the various soft supersymmetry breaking
parameters, giving a mixed anomaly-gravity mediation model. We consider the
pattern of masses that are governed by these soft terms and investigate the
implications of certain indirect constraints on supersymmetric models. In this
framework, we point out how the complementarity between direct and indirect
detection of a neutralino Dark Matter, and futur accelerator prospects can
reduce considerably the parameter space of such models
