A phylogenetic tree comprising clades with high bootstrap values or other strong measures of statistical support is usually interpreted as providing a good estimate of the true phylogeny. Convergent evolution acting on groups of characters in concert, however, can lead to highly supported but erroneous phylogenies. Identifying such groups of phylogenetically misleading characters is obviously desirable. Here we present a procedure that uses an independent data source to identify sets of characters that have undergone concerted convergent evolution. We examine the problematic case of the cormorants and shags, for which trees constructed using osteological and molecular characters both have strong statistical support and yet are fundamentally incongruent. We find that the osteological characters can be separated into those that fit the phylogenetic history implied by the molecular data set and those that do not. Moreover, these latter nonfitting osteological characters are internally consistent and form groups of mutually compatible characters or "cliques," which are significantly larger than cliques of shuffled characters. We suggest, therefore, that these cliques of characters are the result of similar selective pressures and are a signature of concerted convergence.