A new model for simulation of rainfall time series is proposed. It is shown that both the intensity and duration of individual rainfall events can be best modeled by a “fat-tailed” Levy-stable distribution. The temporal downscaling of individual events is produced by a new type of a bounded random cascade model. The proposed rainfall model is shown to successfully reproduce the statistical behavior of individual storms as well as, and in particular, the statistical behavior of annual maxima. In contrast, a model based on a gamma distribution for rainfall intensity substantially underestimates the absolute values of extreme events and does not correctly reproduce their scaling behavior. Similarly, a model based on self-similar random cascade (as opposed to the bounded cascade) substantially overestimates the extreme events.