Large-scale public health trials are often randomized by geographic or administrative clusters, for reasons of financial or organizational exigency. In this paper, we deal with the situation where the dependent variable is a count of events, such as mortality from, or incidence of a given disease. Simulation results show that this design may decrease power by more than 50 per cent. The lost power can largely be replaced by incorporating information on the dependent variable, within clusters, before the start of the trial. The pretrial and trial data can be analysed by negative trinomial models.