  We study the effects of a non thermal neutralino production, due to the late
decay in the early universe of a single modulus field, in the context of the
deflected anomaly mediated scenario. In the regime in which the average number
of neutralino produced in each modulus decaying process is $\bar{N}_{{\rm
LSP}}\ll 1$ also models with a thermal relic density below WMAP data became
acceptable models. We find out that these models belong to three different
classes with the common feature that the low thermal relic density is entirely
due to coannihilation effects. The neutralino annihilation cross section for
these classes of models is not particularly high compared with the highest
cross sections attainable in the generic framework of the MSSM. Hence the
detection prospects either by direct or indirect WIMP search experiments are
not encouraging.
