Since the development of a common mechanism model for non-molecular data in 2001 there has been an alternative to the Parsimony model for phylogenetic analyses of morphological data. In this talk these two approaches to phylogenetic inference are compared. The history and mechanism of each model is described. Model-fitting approaches to identify best-fitting models are described in the context of morphological data. Performance attributes are compared and in conclusion the Parsimony model is found to be most useful as a data-exploration method, due to its speed. Whereas the Mkv model is found to be the best justified method to conduct final analyses for publication.