Many of the eukaryotic phylogenomic analyses published to date were based on alignments of hundreds to thousands of genes. Frequently, in such analyses, the most realistic evolutionary models currently available are often used to minimize the impact of systematic error. However, controversy remains over whether or not idiosyncratic gene family dynamics (i.e., gene duplications and losses) and incorrect orthology assignments are always appropriately taken into account. In this paper, we present an innovative strategy for overcoming orthology assignment problems. Rather than identifying and eliminating genes with paralogy problems, we have constructed a data set comprised exclusively of conserved single-copy protein domains that, unlike most of the commonly used phylogenomic data sets, should be less confounded by orthology miss-assignments. To evaluate the power of this approach, we performed maximum likelihood and Bayesian analyses to infer the evolutionary relationships within the opisthokonts (which includes Metazoa, Fungi, and related unicellular lineages). We used this approach to test 1) whether Filasterea and Ichthyosporea form a clade, 2) the interrelationships of early-branching metazoans, and 3) the relationships among early-branching fungi. We also assessed the impact of some methods that are known to minimize systematic error, including reducing the distance between the outgroup and ingroup taxa or using the CAT evolutionary model. Overall, our analyses support the Filozoa hypothesis in which Ichthyosporea are the first holozoan lineage to emerge followed by Filasterea, Choanoflagellata, and Metazoa. Blastocladiomycota appears as a lineage separate from Chytridiomycota, although this result is not strongly supported. These results represent independent tests of previous phylogenetic hypotheses, highlighting the importance of sophisticated approaches for orthology assignment in phylogenomic analyses.