The Mkv evolutionary model, based on minor modifications to models of molecular evolution, is being increasingly used to infer phylogenies from discrete morphological data, often producing different results from parsimony. The critical difference between Mkv and parsimony is the assumption of a “common mechanism” in the Mkv model, with branch lengths determining that probability of change for all characters increases or decreases at the same tree branches by the same exponential factor. We evaluate whether the assumption of a common mechanism applies to morphology, by testing the implicit prediction that branch lengths calculated from different subsets of characters will be significantly correlated. Our analysis shows that DNA (38 datasets tested) is often compatible with a common mechanism, but morphology (86 datasets tested) generally is not, showing very disparate branch lengths for different character partitions. The low levels of branch length correlation demonstrated for morphology (fitting models without a common mechanism) suggest that the Mkv model is too unrealistic and inadequate for the analysis of most morphological datasets.