Models and physical reasoning predict that extreme precipitation will increase in a warmer climate due to increased atmospheric humidity1, 2, 3. Observational tests using regression analysis have reported a puzzling variety of apparent scaling rates including strong rates in midlatitude locations but weak or negative rates in the tropics4, 5. Here we analyse daily extreme precipitation events in several Australian cities to show that temporary local cooling associated with extreme events and associated synoptic conditions reduces these apparent scaling rates, especially in warmer climatic conditions. A regional climate projection ensemble6 for Australia, which implicitly includes these effects, accurately and robustly reproduces the observed apparent scaling throughout the continent for daily precipitation extremes. Projections from the same model show future daily extremes increasing at rates faster than those inferred from observed scaling. The strongest extremes (99.9th percentile events) scale significantly faster than near-surface water vapour, between 5.7–15%°C−1 depending on model details. This scaling rate is highly correlated with the change in water vapour, implying a trade-off between a more arid future climate or one with strong increases in extreme precipitation. These conclusions are likely to generalize to other regions.