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.