  We examine the relic density of the light mass dark matter region in the
inert doublet model (IDM) when the dominant process is due to co-annihilation
between the lightest neutral scalars of the model. The full one-loop
electroweak corrections are computed in an on-shell scheme and are found to be
well approximated as an effective cross-section expressed in terms of
$Z$-observables. The electroweak corrections to the subdominant process which
consists of an annihilation into an on-shell $W$ and an off-shell $W$, that is
calculated as a annihilation into a 3-body final state, is also performed. The
latter reveals an important dependence on a parameter that describes the
self-interaction of the new scalars (solely within the dark sector), a
parameter which is not accessible in tree-level calculations of standard model
(SM)-IDM interactions.
