The linearity of global-mean outgoing longwave radiation (OLR) with surface temperature is a basic assumption in climate dynamics. This linearity manifests in global climate models, which robustly produce a global-mean longwave clear-sky (LWCS) feedback of 1.9 W/m2/K, consistent with idealized single-column models (Koll & Cronin, 2018, https//:doi.org/10.1073/pnas.1809868115). However, there is considerable spatial variability in the LWCS feedback, including negative values over tropical oceans (known as the “super-greenhouse effect”) which are compensated for by larger values in the subtropics/extratropics. Therefore, it is unclear how the idealized single-column 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 free-tropospheric column RH is largely invariant under warming. ©2020. American Geophysical Union. All Rights Reserved.