The credibility of changes to daily precipitation extremes in model projections is addressed by evaluation of historical performance and a study of model agreement on changes to the full distribution across process-based regimes. The CMIP5 daily precipitation distribution for rain rates exceeding the observed 95th percentile is evaluated against satellite-derived estimates. The rain rates considered include most of the bins that contribute substantially to the total amount, and exclude principally light precipitation. After excluding light precipitation, many models produce daily precipitation distributions that are consistent with observational estimates, and some do so even in the tropics where many models struggle. Past studies have often divided the world based on latitude as a crude proxy for precipitation regimes. Here we employ a novel process-based division beginning with regimes in which large-scale or convective precipitation dominates. We further divide convective-dominated regions based on the sign of the projected change in variance, which has been shown to correlate with changes to extreme precipitation (Pendergrass et al 2017). In locations where models agree that large-scale precipitation dominates, there is remarkable agreement between models on the distribution of daily precipitation amount across rain rate bins in the historical period, and on the change under RCP8.5. The agreement is better in the Northern extra-tropics, where models also agree that the convective fraction will increase in the future. In all regimes, except for where variance decreases, models agree that the higher the rain rate, the greater the percent increase in precipitation in the latter part of the 21st century under RCP8.5. Our summarization offers guidance on where and when projections of changes to extreme precipitation have greater credibility due to a combination of historical performance and multi-model agreement.