Climate models robustly imply that some significant change in precipitation patterns will occur. Models consistently project that the intensity of individual precipitation events increases by approximately 6-7%/K, following the increase in atmospheric water content, but that total precipitation increases by a lesser amount (2-3%/K in the global average). Some other aspect of precipitation events must then change to compensate for this difference. We develop here a new methodology for identifying individual rainstorms and studying their physical characteristics - including starting location, intensity, spatial extent, duration, and trajectory - that allows identifying that compensating mechanism. We apply this technique to precipitation over the contiguous U.S. from both radar-based data products and high-resolution model runs simulating 100 years of business-as-usual warming. In model studies, we find that the dominant compensating mechanism is a reduction of storm size. In summer, rainstorms become more intense but smaller, in winter, rainstorm shrinkage still dominates, but storms also become less numerous and shorter duration. These results imply that flood impacts from climate change will be less severe than would be expected from changes in precipitation intensity alone. We show also that projected changes are smaller than model-observation biases, implying that the best means of incorporating them into impact assessments is via "data-driven simulations" that apply model-projected changes to observational data. We therefore develop a simulation algorithm that statistically describes model changes in precipitation characteristics and adjusts data accordingly, and show that, especially for summertime precipitation, it outperforms simulation approaches that do not include spatial information.