Summary. Data obtained describing terrorist events are particularly difficult to analyse, owing to the many problems that are associated with the data collection process, the inherent variability in the data themselves and the usually poor level of measurement coming from observing political actors who seek not to provide reliable data on their activities. Thus, there is a need for sophisticated modelling to obtain reasonable inferences from these data. Here we develop a logistic random-effects specification using a Dirichlet process to model the random effects. We first look at how such a model can best be implemented, and then we use the model to analyse terrorism data. We see that the richer Dirichlet process random-effects model, compared with a normal random-effects model, can remove more of the underlying variability from the data, uncovering latent information that would not otherwise have been revealed.