The reconstruction of phylogenetic trees from molecular sequences presents unusual problems for statistical inference. For example, three possible alternatives must be considered for four taxa when inferring the correct unrooted tree (referred to as a topology). In our view, classical hypothesis testing is poorly suited to this triangular set of alternative hypotheses. In this article, we develop Bayesian inference to determine the posterior probability that a four-taxon topology is correct given the sequence data and the evolutionary parsimony algorithm for phylogenetic reconstruction. We assess the frequency properties of our models in a large simulation study. Bayesian inference under the principles of evolutionary parsimony is shown to be well calibrated with reasonable discriminating power for a wide range of realistic conditions, including conditions that violate the assumptions of evolutionary parsimony.