Climate change is expected to impact not only the total amount, but also the frequency and intensity of rainfall on regional to global scales. Global climate models that diagnostically parameterize deep convection have been widely used to investigate how rainfall statistics will change in the future despite the problem that they struggle to capture these characteristics when compared to observed present-day precipitation. Here we analyze daily rainfall and its response to climate change using “cloud super- parameterization” (SP), in which convective and boundary layer processes are simulated by embedded cloud-resolving models rather than approximated by conventional parameterizations. We discriminate robust effects of SP by analyzing several statistics of the rainfall frequency and amount distributions (mean rainfall, dry day frequency, rainfall intensity, and rainfall amount mode) in three conventional and super-parameterized versions of the Community Atmosphere Model (CAM and SPCAM) including (SP)CCSM4, (SP)CESM1-CAM4, and (SP)CESM1-CAM5. Little improvement in mean state biases is seen with super-parameterization, but several key secondary characteristics are improved. Importantly, the “amount mode” (the rain rate that delivers the most accumulated rain), which is systematically too weak in CAM, is improved in SPCAM. SPCAM also better captures extreme rain rates, with satisfying insensitivity to horizontal resolution, unlike standard CAM. Poleward of 50 degrees, where a high fraction of rainfall is produced by resolved-scale processes in CAM, few differences discriminate SPCAM vs. CAM daily rainfall properties. However in the tropics, where the convective parameterization produces the majority of rainfall, CAM has a distorted rainfall climate change response. The amount distribution does not smoothly shift right toward more intense rates as it does in SPCAM, but rather increases only the intense rain (large-scale) rates without altering moderate rain (parameterized) rates.