A detailed analysis of some rainfall data from Denver, Colorado, is carried out at different levels of aggregation which range from 1 to 24 hours. Two classes of models are then fitted to the data. In the first class of models, storm events arise in a Poisson process, each such event being associated with a period of rainfall of random duration and constant but random intensity. Total rainfall intensity is formed by adding the contributions from all storm events. In the second class of models, storms arise in a Poisson process, each storm giving rise to a cluster of rain cells and each cell having a random duration and constant but random intensity. The estimation of the model parameters is performed through the first and second-order moments of the cumulative rainfall process at different levels of aggregation. It is found that the first class of models gives a poor fit at levels of aggregation different from the one at which the model parameters are estimated. Cluster-based models are able to take account of the cumulative rainfall characteristics over a range of time scales from 1 to 24 hours without changing the model parameters. These models also perform well in regard to the extreme values of rainfall for different periods of aggregation and the time concentration of total rainfall. ¿American Geophysical Union 1987