This paper describes a method for planning the duration of a randomized parallel group study in which the response of interest is a potentially recurrent event. At the design stage we assume patients accrue at a constant rate, we model events via a homogeneous Poisson process, and we utilize an independent exponential censoring mechanism to reflect loss to follow-up. We derive the appropriate study duration to ensure satisfaction of power requirements for the effect size of interest under a Poisson regression model. An application to a kidney transplant study illustrates the potential savings of the Poisson-based design relative to a design based on the time to the first event. Revised design criteria are also derived to accommodate overdispersed Poisson count data. We examine the frequency properties of two non-parametric tests recently proposed by Lawless and Nadeau for trials based on the above design criteria. In simulation studies involving homogeneous and non-homogeneous Poisson processes they performed well with respect to their type I error rate and power. Results from supplementary simulation studies indicate that these tests are also robust to extra-Poisson variation and to clustering in the event times, making these tests attractive in their generality. We illustrate both tests by application to data from a completed kidney transplant study.