Rainfall intensity extremes are relevant to many aspects of climatology, climate change, and landsurface processes. Intensity is described and analysed using a diversity of approaches, reflecting its importance in these diverse areas. The characteristics of short-interval intensity extremes, such as the maximum 5-min intensity, are explored here. It is shown that such indices may have marked diurnal cycles, as well as seasonal variability. Some indices of intensity, such as the SDII (simple daily intensity index), provide too little information for application to landsurface processes. Upper percentiles of the intensity distribution, such as the 95th and 99th percentiles (Q95 and Q99) are used as indices of extreme intensity, but problematically are affected by changes in intensity below the nominated threshold, as well as above it, making the detection of secular change, and application to sites with contrasting rainfall character, challenging. For application to landsurface processes, a new index is introduced. This index (R Q95 ), is that intensity or rainfall rate above which 5% of the total rainfall is delivered. This index better reflects intense rainfall than does Q95 of even 5-min accumulation duration (AD) rainfall depths. Such an index is helpful for detecting secular change at an observing station, but, like Q95, remains susceptible to the effects of change elsewhere in the distribution of intensities. For understanding impacts of climate and climate change on landsurface processes, it is argued that more inclusive indices of intensity are required, including fixed intensity criteria.