While some aspects of the phylogeny of the five living echinoderm classes are clear, the position of the ophiuroids (brittlestars) relative to asteroids (starfish), echinoids (sea urchins) and holothurians (sea cucumbers) is controversial. Ophiuroids have a pluteus-type larva in common with echinoids giving some support to an ophiuroid/echinoid/holothurian clade named Cryptosyringida. Most molecular phylogenetic studies, however, support an ophiuroid/asteroid clade (Asterozoa) implying either convergent evolution of the pluteus or reversals to an auricularia-type larva in asteroids and holothurians. A recent study of 10 genes from four of the five echinoderm classes used 'phylogenetic signal dissection' to separate alignment positions into subsets of (i) suboptimal, heterogeneously evolving sites (invariant plus rapidly changing) and (ii) the remaining optimal, homogeneously evolving sites. Along with most previous molecular phylogenetic studies, their set of heterogeneous sites, expected to be more prone to systematic error, support Asterozoa. The homogeneous sites, in contrast, support an ophiuroid/echinoid grouping, consistent with the cryptosyringid clade, leading them to posit homology of the ophiopluteus and echinopluteus. Our new dataset comprises 219 genes from all echinoderm classes; analyses using probabilistic Bayesian phylogenetic methods strongly support Asterozoa. The most reliable, slowly evolving quartile of genes also gives highest support for Asterozoa; this support diminishes in second and third quartiles and the fastest changing quartile places the ophiuroids close to the root. Using phylogenetic signal dissection, we find heterogenous sites support an unlikely grouping of Ophiuroidea + Holothuria while homogeneous sites again strongly support Asterozoa. Our large and taxonomically complete dataset finds no support for the cryptosyringid hypothesis; in showing strong support for the Asterozoa, our preferred topology leaves the question of homology of pluteus larvae open.