The relationship between three biologically important groups, arthropods, nematodes, and deuterostomes, remains unresolved. It is unknown whether arthropods are more closely related to nematodes (consistent with the "ecdysozoa" hypothesis) or to deuterostomes (consistent with "coelomata"). We present a method in which we use the pattern of spliceosomal intron conservation to develop a series of inequalities that characterize each possible relationship. We find that only the ecdysozoa grouping satisfies these predictions, with P < 10(-6). Simulations show that our method, unlike some previous methods, is largely insensitive to rate variation between branches.