Maximum likelihood is a common method of estimating a phylogenetic tree based on a set of genetic data. However, models of evolution for certain types of genetic data are highly flawed in their specification, and this misspecification can have an adverse impact on phylogenetic inference. Our attention here is focused on extending an existing class of models for estimating phylogenetic trees from discrete morphological characters. The main advance of this work is a model that allows unequal equilibrium frequencies in the estimation of phylogenetic trees from discrete morphological character data using likelihood methods. Possible extensions of the proposed model will also be discussed.