The problem of missing data is often considered to be the most important obstacle in reconstructing the phylogeny of fossil taxa and in combining data from diverse characters and taxa for phylogenetic analysis. Empirical and theoretical studies show that including highly incomplete taxa can lead to multiple equally parsimonious trees, poorly resolved consensus trees, and decreased phylogenetic accuracy. However, the mechanisms that cause incomplete taxa to be problematic have remained unclear. It has been widely assumed that incomplete taxa are problematic because of the proportion or amount of missing data that they bear. In this study, I use simulations to show that the reduced accuracy associated with including incomplete taxa is caused by these taxa bearing too few complete characters rather than too many missing data cells. This seemingly subtle distinction has a number of important implications. First, the so-called missing data problem for incomplete taxa is, paradoxically, not directly related to their amount or proportion of missing data. Thus, the level of completeness alone should not guide the exclusion of taxa (contrary to common practice), and these results may explain why empirical studies have sometimes found little relationship between the completeness of a taxon and its impact on an analysis. These results also (1) suggest a more effective strategy for dealing with incomplete taxa, (2) call into question a justification of the controversial phylogenetic supertree approach, and (3) show the potential for the accurate phylogenetic placement of highly incomplete taxa, both when combining diverse data sets and when analyzing relationships of fossil taxa.