Computer simulation was employed to explore the discharge behavior of one- and two-compartment models of a cerebellar Purkinje cell in response to climbing fiber and current pulse stimulation. We could not find a unique parameter set for any model that replicated the full temporal detail of reported discharge patterns. However, a new composite model cell gave a better overall match to empirical data than similar models employing the more realistic Hodgkin-Huxley description of conductances. The better match achieved by the simpler models suggests that the composite level of description is well suited to simulation of neuronal discharge patterns and the temporal detail required for the realistic functional exploration of large scale neuronal networks.