By various measures (drought area and intensity, climatic aridity index, and climatic water deficits), some observational analyses have suggested that much of the Earth’s land has been drying during recent decades, but such drying seems inconsistent with observations of dryland greening and decreasing pan evaporation. ‘Offline’ analyses of climate-model outputs from anthropogenic climate change (ACC) experiments portend continuation of putative drying through the twenty-first century, despite an expected increase in global land precipitation. A ubiquitous increase in estimates of potential evapotranspiration (PET), driven by atmospheric warming, underlies the drying trends, but may be a methodological artefact. Here we show that the PET estimator commonly used (the Penman–Monteith PET for either an open-water surface or a reference crop) severely overpredicts the changes in non-water-stressed evapotranspiration computed in the climate models themselves in ACC experiments. This overprediction is partially due to neglect of stomatal conductance reductions commonly induced by increasing atmospheric CO₂ concentrations in climate models. Our findings imply that historical and future tendencies towards continental drying, as characterized by offline-computed runoff, as well as other PET-dependent metrics, may be considerably weaker and less extensive than previously thought.