  Dark matter (DM) as a thermal relic of the primordial plasma is increasingly
pressured by direct and indirect searches, while the same production mechanism
in a decoupled sector is much less constrained. We extend the standard
treatment of the freeze-out process to such scenarios and perform precision
calculations of the annihilation cross-section required to match the observed
DM abundance. We demonstrate that the difference to the canonical value of this
'thermal cross-section' is generally sizeable, and can reach orders of
magnitude. Our results directly impact the interpretation of DM searches in
hidden sector scenarios.
