Resolving the relationships between the major lineages in the animal tree of life is necessary to understand the origin and evolution of key animal traits. Sponges, characterized by their simple body plan, were traditionally considered the sister group of all other animal lineages, implying a gradual increase in animal complexity from unicellularity to complex multicellularity. However, the availability of genomic data has sparked tremendous controversy as some phylogenomic studies support comb jellies taking this position, requiring secondary loss or independent origins of complex traits. Here we show that incorporating site-heterogeneous mixture models and recoding into partitioned phylogenomics alleviates systematic errors that hamper commonly-applied phylogenetic models. Testing on real datasets, we show a great improvement in model-fit that attenuates branching artefacts induced by systematic error. We reanalyse key datasets and show that partitioned phylogenomics does not support comb jellies as sister to other animals at either the supermatrix or partition-specific level.