Acoel flatworms are small marine worms traditionally considered to belong to the phylum Platyhelminthes. However, molecular phylogenetic analyses suggest that acoels are not members of Platyhelminthes, but are rather extant members of the earliest diverging Bilateria. This result has been called into question, under suspicions of a long branch attraction (LBA) artefact. Here we re-examine this problem through a phylogenomic approach using 68 different protein-coding genes from the acoel Convoluta pulchra and 51 metazoan species belonging to 15 different phyla. We employ a mixture model, named CAT, previously found to overcome LBA artefacts where classical models fail. Our results unequivocally show that acoels are not part of the classically defined Platyhelminthes, making the latter polyphyletic. Moreover, they indicate a deuterostome affinity for acoels, potentially as a sister group to all deuterostomes, to Xenoturbellida, to Ambulacraria, or even to chordates. However, the weak support found for most deuterostome nodes, together with the very fast evolutionary rate of the acoel Convoluta pulchra, call for more data from slowly evolving acoels (or from its sister-group, the Nemertodermatida) to solve this challenging phylogenetic problem.