Equations for a diffusion neuronal model describing the production of nerve impulses have been derived for the case in which the noisy depolarizations of the membrane potential are restricted by the reversal potentials. Identifying neuron firing intervals with the first-passage-time distribution for the associated process allows us to compute the interspike interval statistics and relate them to the parameters characterizing the neuronal input. Methods for approximation of the first two moments of the interspike intervals are proposed. The analytical results are numerically illustrated and simultaneous computer simulations were performed for the same purpose. A comparison of the achieved results is made with those from other diffusion models or the models with discontinuous trajectories. The model is proposed mainly as an alternative to the Ornstein-Uhlenbeck neuronal model.