While daily extreme precipitation intensities increase with global warming on average at approximately the same rate as the availability of water vapor (~7%/°C), a debated topic is whether sub-daily extremes increase more. Modelling at convection-permitting scales has been deemed necessary to reproduce extreme summer precipitation at local scale. Here we analyze multi-model ensembles and apply a 3 km horizontal resolution model over four regions across Europe (S. Norway, Denmark, Benelux and Albania) and find very good agreement with observed daily and hourly summer precipitation extremes. Projections show that daily extreme precipitation intensifies compared to the mean in all regions and across a wide range of models and resolutions. Hourly and 10 min extremes intensify at a higher rate in nearly all regions. Unlike most recent studies, we do not find sub-daily precipitation extremes increasing much more than 7%/°C, even for sub-hourly extremes, but this may be due to robust summer drying over large parts of Europe. However, the absolute strongest local daily precipitation event in a 20 year period will increase by 10%–20%/°C. At the same time, model projections strongly indicate that summer drying will be more pronounced for extremely dry years.