  We consider dark matter (DM) with very weak couplings to the standard model
(SM), such that its self-annihilation cross section is much smaller than the
canonical one, $\langle\sigma v\rangle_{\chi\chi} \ll
10^{-26}\mathrm{cm}^3/\mathrm{s}$. In this case DM self-annihilation is
negligible for the dynamics of freeze-out and DM dilution is solely driven by
efficient annihilation of heavier accompanying dark sector particles provided
that DM maintains chemical equilibrium with the dark sector. This chemical
equilibrium is established by conversion processes which require much smaller
couplings to be efficient than annihilation. The chemical decoupling of DM from
the SM can either be initiated by the freeze-out of annihilation, resembling a
co-annihilation scenario, or of conversion processes, leading to the scenario
of conversion-driven freeze-out. We focus on the latter and discuss its
distinct phenomenology.
