Understanding the drivers of precipitation and their changes in a non-stationary climate is crucial for effective climate adaptation and water resource management, as it helps us anticipate and respond to shifting precipitation patterns and their impacts. Here, analysing simulations from the Coupled Model Intercomparison Project Phase 6 (CMIP6) we show that the conditional probability of extreme daily precipitation given joint extremes of two drivers (precipitable water and vertical velocity) will be stable in a 3 °C warmer future. Consistent with earlier work, we find that the near-global increase in precipitable water (thermodynamic influence) is the baseline for changes in extreme precipitation, which are modulated by changes in vertical velocity (dynamic influence). Thus, in regions where vertical velocity increases, the effect of the two drivers is additive and their changes contribute to an increase in extreme precipitation. The changes of the two drivers are opposite where vertical velocity decreases, resulting in only small increases in extreme precipitation or even a decrease. Furthermore, we reveal that there are moderate changes in the dependence between the drivers, which are larger over the ocean than over landmasses, but they contribute only little to the overall changes in extreme precipitation. We conclude that the use of two very simple drivers that are readily available from climate models can be of great utility for evaluating precipitation extremes in models and understanding their projected changes.