A good approximation to the integrate-and-fire model with diffusive noise can be obtained using a noisy threshold model. This allows the response of a population of noisy neurons to a current transient to be described using a linear filter. Here we apply these analytical results to the peristimulus time histogram (PSTH) of a single neuron. The effect of the noise on the PSTH in our model is similar to that seen in experimental findings of Poliakov et al. (J. Physiol., Part 1,495 (1996) 143–157) on hypoglossal and cat lumbar motoneurons and could help in interpreting their results.