The problems encountered when using traditional rectangular pulse hierarchical point process models for fine temporal resolution and the growing number of available tip-time records suggest that rainfall increments from tipping-bucket gauges be modelled directly. Poisson processes are used with an arrival rate modulated by a Markov chain in continuous time. The paper shows how, by using two or three states for this chain, much of the structure of the rainfall intensity distribution and the wet/dry sequences can be represented for time-scales as small as 5 minutes.