Two simple kinetic models of a Ne-buffered XeCl laser discharge are presented based on different simplifications of the chemical kinetics of a complex model that recently appeared in the literature. when applied to the study of a small-volume XeCl laser, the results of both simple and complex models are in satisfactory agreement with the experiments. Shifting to a larger-volume laser, both models show problems due to loss of stability of the discharge. A one-dimensional modeling is performed, and it is found that different assumptions on the kinetics of the NeXe+ ion in the discharge lead to completely different results as regards the effect of a preionization-triggered instability.