The change of global-mean precipitation under global warming and interannual variability is predominantly controlled by the change of atmospheric longwave radiative cooling. Here we show that tightening of the ascending branch of the Hadley Circulation coupled with a decrease in tropical high cloud fraction is key in modulating precipitation response to surface warming. The magnitude of high cloud shrinkage is a primary contributor to the intermodel spread in the changes of tropical-mean outgoing longwave radiation (OLR) and global-mean precipitation per unit surface warming (d
P/d Ts) for both interannual variability and global warming. Compared to observations, most Coupled Model Inter-comparison Project Phase 5 models underestimate the rates of interannual tropical-mean dOLR/d Ts and global-mean d P/d Ts, consistent with the muted tropical high cloud shrinkage. We find that the five models that agree with the observation-based interannual d P/d Ts all predict d P/d Ts under global warming higher than the ensemble mean d P/d Ts from the ∼20 models analysed in this study.