Instances of intense rain rates pose substantial risks to life and property. Recent studies have shown that such high-impact rain events tend to occur as components within larger rain systems. However, it is less clear what importance the spatial arrangement -- the morphology -- of the precipitation within these systems has on the generation of such events. Using observations of tropical precipitation obtained from satellites, we show that the more spatially localized the rain production within a system is, the more intense its maximum rain rate, regardless of the size of the system. We further use output from a global high-resolution model to investigate the importance of both the large-scale environment and the local-scale inhomogeneity of surface moisture and temperature in the generation of such extreme events.