Xenoturbella and the acoelomorph worms (Xenacoelomorpha) are simple marine animals with controversial affinities. They have been placed as the sister group of all other bilaterian animals (Nephrozoa hypothesis), implying their simplicity is an ancient characteristic [1, 2]; alternatively, they have been linked to the complex Ambulacraria (echinoderms and hemichordates) in a clade called the Xenambulacraria [3-5], suggesting their simplicity evolved by reduction from a complex ancestor. The difficulty resolving this problem implies the phylogenetic signal supporting the correct solution is weak and affected by inadequate modeling, creating a misleading non-phylogenetic signal. The idea that the Nephrozoa hypothesis might be an artifact is prompted by the faster molecular evolutionary rate observed within the Acoelomorpha. Unequal rates of evolution are known to result in the systematic artifact of long branch attraction, which would be predicted to result in an attraction between long-branch acoelomorphs and the outgroup, pulling them toward the root [6]. Other biases inadequately accommodated by the models used can also have strong effects, exacerbated in the context of short internal branches and long terminal branches [7]. We have assembled a large and informative dataset to address this problem. Analyses designed to reduce or to emphasize misleading signals show the Nephrozoa hypothesis is supported under conditions expected to exacerbate errors, and the Xenambulacraria hypothesis is preferred in conditions designed to reduce errors. Our reanalyses of two other recently published datasets [1, 2] produce the same result. We conclude that the Xenacoelomorpha are simplified relatives of the Ambulacraria.