The origin of the eukaryotic genetic apparatus is thought to be central to understanding the evolution of the eukaryotic cell. Disagreement about the source of the relevant genes has spawned competing hypotheses for the origins of the eukaryote nuclear lineage. The iconic rooted 3-domains tree of life shows eukaryotes and archaebacteria as separate groups that share a common ancestor to the exclusion of eubacteria. By contrast, the eocyte hypothesis has eukaryotes originating within the archaebacteria and sharing a common ancestor with a particular group called the Crenarchaeota or eocytes. Here, we have investigated the relative support for each hypothesis from analysis of 53 genes spanning the 3 domains, including essential components of the eukaryotic nucleic acid replication, transcription, and translation apparatus. As an important component of our analysis, we investigated the fit between model and data with respect to composition. Compositional heterogeneity is a pervasive problem for reconstruction of ancient relationships, which, if ignored, can produce an incorrect tree with strong support. To mitigate its effects, we used phylogenetic models that allow for changing nucleotide or amino acid compositions over the tree and data. Our analyses favor a topology that supports the eocyte hypothesis rather than archaebacterial monophyly and the 3-domains tree of life.