The Mk model was developed for estimating phylogenetic trees from discrete morphological data, whether for living or fossil taxa. Like any model, the Mk model makes a number of assumptions. One assumption is that transitions between character states are symmetric (i.e., the probability of changing from 0 to 1 is the same as 1 to 0). However, some characters in a data matrix may not satisfy this assumption. Here, we test methods for relaxing this assumption in a Bayesian context. Using empirical datasets, we perform model fitting to illustrate cases in which modeling asymmetric transition rates among characters is preferable to the standard Mk model. We use simulated datasets to demonstrate that choosing the best-fit model of transition-state symmetry can improve model fit and phylogenetic estimation.