Understanding how the outgoing long-wave radiation (OLR) depends on surface temperature is a climate problem of long standing. Various studies have suggested that clear-sky OLR varies linearly with surface temperature, with a longwave clear-sky feedback that is independent of surface temperature and relative humidity. However, this uniformity lies in tension with the notion that humidity controls tropical stability (e.g. the “furnace” and “radiator fins” of Pierrehumbert, 1995). Here we explore the state-dependence of longwave clear-sky feedback as a function of both surface temperature and column relative humidity. We find that a strong relative humidity-dependence in the feedback emerges above 275 K, stemming from the closing of the H2O window. We construct a simple model for estimating the all-sky feedback and find that although clouds lower the zonal-mean longwave feedback, the dependence on humidity remains significant.