Precipitation changes are a key driver of climate change impacts. On average, global precipitation is expected to increase with warming. However, model projections show that precipitation does not scale linearly with surface air temperature. Instead, global hydrological sensitivity, the relative change of global-mean precipitation per degree of global warming, seems to vary across different scenarios and even with time. Based on output from 20 coupled Atmosphere-Ocean-General-Circulation-Models for up to 7 different scenarios, we discuss to what extent these variations can be explained by changes in the tropospheric energy budget. Our analysis supports earlier findings that long- and shortwave absorbers initially decrease global-mean precipitation. Including these absorbers into a multivariate scaling approach allows to closely reproduce the simulated global-mean precipitation changes. We find a sensitivity of global-mean precipitation to tropospheric greenhouse gas forcing of −0.42 ± 0.23%/(W/m2) (uncertainty given as one std of inter-model variability) and to black carbon emissions of −0.07 ± 0.02%/(Mt/yr). In combination with these two predictors the dominant longer-term effect of surface air temperatures on precipitation is estimated to be 2.2 ± 0.52%/K – much lower than the 6.5%/K that may be expected from the Clausius-Clapeyron relationship.