  In the simplest models of asymmetric dark matter (ADM) annihilation signals
are not expected, since the DM is non-self-conjugate and the relic density of
anti-DM is negligible. We investigate a new class of models in which a
symmetric DM component, in the `low-mass' 1-10 GeV regime favoured for linking
the DM and baryon asymmetries, is repopulated through decays. We find that, in
models without significant velocity dependence of the annihilation cross
section, observational constraints generally force these decays to be
(cosmologically) slow. These late decays can give rise to gamma-ray signal
morphologies differing from usual annihilation profiles. A distinctive feature
of such models is that signals may be absent from dwarf spheroidal galaxies.
