Poisson processes are adequate descriptions of spike trains pooled across large numbers of trials. When probabilities are needed to describe the behavior of neurons within individual trials, however, Poisson process models are often inadequate. In principle, an explicit formula gives the probability density of a single spike train for a general counting process, but without additional assumptions the intensity function appearing in that formula can not be estimated. We propose a simple solution to this problem, which is to assume that the time at which a neuron fires is determined probabilistically by, and only by, two quantities: the experimental clock time and the time since the last spike. We show that this model may be used successfully to fit neuronal data.