The relationships at the root of the animal tree have proven difficult to resolve, with the current debate focusing on whether sponges (phylum Porifera) or comb jellies (phylum Ctenophora) are the sister group of all other animals [1-5]. The choice of evolutionary models seems to be at the core of the problem because Porifera tends to emerge as the sister group of all other animals ("Porifera-sister") when site-specific amino acid differences are modeled (e.g., [6, 7]), whereas Ctenophora emerges as the sister group of all other animals ("Ctenophora-sister") when they are ignored (e.g., [8-11]). We show that two key phylogenomic datasets that previously supported Ctenophora-sister [10, 12] display strong heterogeneity in amino acid composition across sites and taxa and that no routinely used evolutionary model can adequately describe both forms of heterogeneity. We show that data-recoding methods [13-15] reduce compositional heterogeneity in these datasets and that models accommodating site-specific amino acid preferences can better describe the recoded datasets. Increased model adequacy is associated with significant topological changes in support of Porifera-sister. Because adequate modeling of the evolutionary process that generated the data is fundamental to recovering an accurate phylogeny [16-20], our results strongly support sponges as the sister group of all other animals and provide further evidence that Ctenophora-sister represents a tree reconstruction artifact. VIDEO ABSTRACT.