Resolving evolutionary relationships in groups that underwent fast radiation in deep time is a problem for molecular phylogeny, as the scant phylogenetic signal that characterises short internal branches is generally swamped by more recent substitutions. We implement an approach, that maps how the support for rival phylogenies changes when analysing subsets of sites with either faster and more heterogeneous rates or slower and more homogeneous rates, to address a long-standing problem in deuterostome phylogeny - the interrelationships of the eleutherozoan echinoderm classes. We show that miRNA genes are phylogenetically uninformative as to the relationships of asteroids, echinoids and ophiuroids, consistent with a rapid radiation of these groups as suggested by their fossil record. Using three nuclear rRNAs and seven nuclear housekeeping genes, we map the support for the three possible phylogenetic arrangements of asteroids, ophiuroids and echinoids when moving between subsets of the data with very similar or very different rates of evolution. Only one of the three possible topologies (asteroids (ophiuroids+echinoids)) strengthens when the most rate-homogeneous subset of data are analysed. The other two possible pairings become stronger in a less reliable data subset, which includes the fastest and thus homoplasy-rich data in our alignment. Thus, while superficial analysis of our concatenated alignment identifies asteroids and ophiuroids as sister taxa, more thorough analyses suggest that ophiuroids may be more closely related to echinoids. Divergence of these echinoderm groups, using a relaxed molecular clock, is estimated to have occurred within ≈ 5 million years. Our results illustrate that the analytic approach of phylogenetic signal dissection can be a powerful tool to investigate rapid radiations in deep geologic time.