When direct measurements of the quantal parameters for a synapse cannot be made, these parameters can be extracted from an analysis of the fluctuations in the evoked response at that synapse. In this article, a decision tree is described in which the ability of the data to match simple models of quantal transmission is rigorously compared with its ability to fit progressively more complex models. The Wilks statistic is the basis for this comparison. The procedure commences with optimal transformation of peak amplitude measurements into a probability density function (PDF). It then examines this PDF against various models of transmission, commencing with a multi-modal but non-quantal distribution, then to a multi-modal distribution with quantal peak separation with and without quantal variability, and, finally, the constraints of uniform and non-uniform release probabilities are imposed. These procedures are illustrated by example. A comparison is made between the relative sensitivities of the Wilks statistic and the chi2 goodness-of-fit criteria in rejecting inappropriate models at all stages in these procedures.