Hard-tissue morphological characters (bones and teeth) are a primary source of information about the evolutionary history of primates. These tissues are commonly found as isolated elements in the fossil record and studied as three separate partitions: the dentition, the cranium, and the postcranium. The relative phylogenetic utility of characters from each partition is often called into question with respect to varying amounts of homoplasy. In this paper, the consistency index (CI) was used to measure levels of homoplasy in each data partition for a sample of fossil and living primates. Sources of bias in the collection and treatment of data and in the internal structure of the data set are addressed. These biases include number of taxa, number of characters, ordering of characters, amounts of polymorphically scored or missing data, and character-state distribution. The results of this study suggest that the levels of homoplasy are very similar, though the postcranial data may be slightly less homoplastic than either the dental or cranial data.