Radiative cooling on the lowest atmospheric levels is of strong importance for modulating atmospheric circulations and organizing convection, but detailed observations and a robust theoretical understanding are lacking. Here we use unprecedented observational constraints from subsidence regimes in the tropical Atlantic to develop a theory for the shape and magnitude of low-level longwave radiative cooling in clear-sky, showing large peaks at the top of the boundary layer. A suite of novel scaling approximations is first developed from simplified spectral theory, in close agreement with the measurements. The radiative cooling peak height is set by the maximum lapse rate in water vapor path, and its magnitude is mainly controlled by the ratio of column relative humidity above and below the peak. We emphasize how elevated intrusions of moist air can reduce low-level cooling, by sporadically shading the spectral range which effectively cools to space. The efficiency of this spectral shading depends both on water content and altitude of moist intrusions; its height dependence cannot be explained by the temperature difference between the emitting and absorbing layers, but by the decrease of water vapor extinction with altitude. This analytical work can help to narrow the search for low-level cloud patterns sensitive to radiative-convective feedbacks: the most organized patterns with largest cloud fractions tend to occur in atmospheres below 10% relative humidity and feel the strongest low-level cooling. This motivates further assessment of these favorable conditions for radiative-convective feedbacks and a robust quantification of corresponding shallow cloud dynamics in current and warmer climates.