The three-domains tree, which depicts eukaryotes and archaebacteria as monophyletic sister groups, is the dominant model for early eukaryotic evolution. By contrast, the 'eocyte hypothesis', where eukaryotes are proposed to have originated from within the archaebacteria as sister to the Crenarchaeota (also called the eocytes), has been largely neglected in the literature. We have investigated support for these two competing hypotheses from molecular sequence data using methods that attempt to accommodate the across-site compositional heterogeneity and across-tree compositional and rate matrix heterogeneity that are manifest features of these data. When ribosomal RNA genes were analysed using standard methods that do not adequately model these kinds of heterogeneity, the three-domains tree was supported. However, this support was eroded or lost when composition-heterogeneous models were used, with concomitant increase in support for the eocyte tree for eukaryotic origins. Analysis of combined amino acid sequences from 41 protein-coding genes supported the eocyte tree, whether or not composition-heterogeneous models were used. The possible effects of substitutional saturation of our data were examined using simulation; these results suggested that saturation is delayed by among-site rate variation in the sequences, and that phylogenetic signal for ancient relationships is plausibly present in these data.