Absorbing aerosols affect global-mean precipitation primarily in two ways. They give rise to stronger shortwave atmospheric heating, which acts to suppress precipitation. Depending on the top-of-the-atmosphere radiative flux change, they can also warm up the surface with a tendency to increase precipitation. Here, we present a theoretical framework that takes into account both effects, and apply it to analyze the hydrological responses to increased black carbon burden simulated with a general circulation model. It is found that the damping effect of atmospheric heating can outweigh the enhancing effect of surface warming, resulting in a net decrease in precipitation. The implications for moist convection and general circulation are discussed.