  Assuming the existence of a primordial asymmetry in the dark sector, a
scenario usually dubbed Asymmetric Dark Matter (aDM), we study the effect of
oscillations between dark matter and its antiparticle on the re-equilibration
of the initial asymmetry before freeze-out, which enable efficient
annihilations to recouple. We calculate the evolution of the DM relic abundance
and show how oscillations re-open the parameter space of aDM models, in
particular in the direction of allowing large (WIMP-scale) DM masses. A typical
wimp with a mass at the EW scale (\sim 100 GeV - 1 TeV) presenting a primordial
asymmetry of the same order as the baryon asymmetry naturally gets the correct
relic abundance if the DM-number-violating Delta(DM) = 2 mass term is in the
\sim meV range. The re-establishment of annihilations implies that constraints
from the accumulation of aDM in astrophysical bodies are evaded. On the other
hand, the ordinary bounds from BBN, CMB and indirect detection signals on
annihilating DM have to be considered.
