The effect of missing data on phylogenetic methods is a potentially important issue in our attempts to reconstruct the Tree of Life. If missing data are truly problematic, then it may be unwise to include species in an analysis that lack data for some characters (incomplete taxa) or to include characters that lack data for some species. Given the difficulty of obtaining data from all characters for all taxa (e.g., fossils), missing data might seriously impede efforts to reconstruct a comprehensive phylogeny that includes all species. Fortunately, recent simulations and empirical analyses suggest that missing data cells are not themselves problematic, and that incomplete taxa can be accurately placed as long as the overall number of characters in the analysis is large. However, these studies have so far only been conducted on parsimony, likelihood, and neighbor-joining methods. Although Bayesian phylogenetic methods have become widely used in recent years, the effects of missing data on Bayesian analysis have not been adequately studied. Here, we conduct simulations to test whether Bayesian analyses can accurately place incomplete taxa despite extensive missing data. In agreement with previous studies of other methods, we find that Bayesian analyses can accurately reconstruct the position of highly incomplete taxa (i.e., 95% missing data), as long as the overall number of characters in the analysis is large. These results suggest that highly incomplete taxa can be safely included in many Bayesian phylogenetic analyses.