We investigate simulated changes of seasonal precipitation maxima and means in a future, warmer climate. We use data from the ESSENCE project, in which a 17-member ensemble of climate change simulations in response to the SRES A1b scenario has been carried out using the ECHAM5/MPI-OM climate model. The large size of the data set gives the opportunity to detect the changes of climate extremes and means with high statistical confidence. Daily precipitation data are used to calculate the seasonal precipitation maximum and the seasonal mean. Modeled precipitation data appear consistent with observation-based data from the Global Precipitation Climatology Project. The data are split into six time periods of 25 years to get independent time series. The seasonal peaks are modeled by using the generalized extreme value distribution, while empirical distributions are used to study changes of the seasonal precipitation mean. Finally, we use an empirical method to detect changes of occurrence of very wet and dry periods. Results from these model simulations indicate that over most of the world precipitation maxima will increase in the future. Seasonal means behave differently. In many regions they are decreasing or not increasing. The occurrence of very wet periods is strongly increasing during boreal winter in the extratropics and decreasing in the tropics. In summary, wet regions become wetter and dry regions become drier.