The linearity of the global-mean outgoing longwave radiation (OLR) with surface temperature has important implications for climate sensitivity. Global climate models robustly produce a 1.9 W/m2/K of global-mean longwave clear-sky (LWCS) feedback. This number is consistent with idealized single-column atmospheric models. However, there is considerable spatial variation in the LWCS feedback including negative values over tropical oceans known as the “super-greenhouse effect” which is compensated by larger values in the subtropics/extratropics. Therefore it is unclear how the idealized model results are relevant for the global-mean LWCS feedback in comprehensive climate models. Here we show with a simple analytical theory and model output that the compensation of this spatial variability to produce a robust global-mean feedback can be explained by two facts: 1) when conditioned upon free-tropospheric column relative humidity (RH), the LWCS feedback is independent of RH, and 2) the global histogram of column RH is largely invariant under warming.