Estimates of phylogenetic relationships among fossil taxa implicitly provide hypotheses about the quality of the fossil record. Phylogenetic inferences also provide hypotheses about character evolution. The likelihood of any hypothesis that makes predictions about two data sets is simply the likelihood of the hypothesis given the first data set times the likelihood of the same hypothesis given the second data set. In this case, data set 1 represents stratigraphy and data set 2 represents morphology. Statistical methods exist for determining the likelihood of hypothesized levels of sampling. The likelihood of a hypothesized amount of character change yielding a particular most-parsimonious solution (i.e, L [hypothesized lengthparsimony length] can be evaluated with simulations. A reanalysis of hyaenid phylogeny based on published character and stratigraphic data is presented here, using the maximum likelihood method. Two trees are found, depending on assumptions about ambiguous species, which are 11 and 10 steps longer than the most parsimonious tree (61 or 60 vs. 50 steps). However, the trees invoke far less stratigraphic debt (9 or 12 units vs. 47 units as measured in Mammal Zones). An important feature of the results is that the most likely tree length given hyaenid character data is estimated to be 56 to 62 steps (depending on the model of character evolution) rather than 50 steps. The likelihood tree suggests stronger trends toward bone-crushing specializations than does the parsimony tree and further suggests that high levels of homoplasy caused parsimony to underestimate the true extent of those trends. Simulations based on the character data and fossil record of hyaenids suggest that the maximum likelihood method is better able to estimate correct trees than is parsimony and somewhat better able to do so than previously proposed phylogenetic methods incorporating stratigraphy.