Phylogenomic studies have improved understanding of deep metazoan phylogeny and show promise for resolving incongruences seen among analyses based on limited numbers of loci. One region of the animal tree that has been hardest to resolve is relationships within Lophotrochozoa, the animal clade that includes molluscs, annelids, and flatworms among others. Lack of resolution could be due to insufficient phylogenetic signal, systematic errors (i.e., noise in the data), or limitations in taxon and/or gene sampling. Thus, we examined relationships within Lophotrochozoa attempting to identify and reduce sources of systematic error. We supplemented existing data with 32 new transcriptomes spanning the diversity of Lophotrochozoa and constructed a new set of Lophotrochozoa-specific core orthologs. Of these, 638 orthologous groups (OGs) passed strict screening for paralogy using a tree-based approach. To discriminate phylogenetic signal from noise resulting from systematic errors, we calculated branch-length heterogeneity, evolutionary rate, missing data, compositional bias, and saturation for each OG and analyzed increasingly stricter subsets of only the best 5/6, 4/6, 3/6, 2/6, and 1/6 of the OGs for these five metrics. OGs were also partitioned into ranked sextiles so that differences in topologies resulting from, for example, analyses of the best 1/6 OGs in terms of missing data could be compared to those from analyses of the worst 1/6. Additional sensitivity analyses examined effects of removing taxa with heterogeneous branch lengths, large amounts of missing data, and compositional heterogeneity. Maximum likelihood (ML) analysis of our complete dataset recovered Annelida + Nemertea sister to Brachiopoda + Phoronida with this clade sister to Mollusca, but support for these relationships was generally weak. However, when genes with high branch length heterogeneity were excluded, ML analyses recovered Annelida sister to Brachiopoda + Phoronida with this clade sister to Mollusca with moderate to strong support. We also attempted to conduct Bayesian inference (BI) analyses using the CAT-GTR model but, despite running nearly six months, the chains failed to converge. Interestingly, these 'preliminary' BI analyses sometimes recovered Lophophorata (a clade of Byrozoa, Phoronida, and Brachiopoda) and Tetraneuralia (Mollusca sister to Entoprocta + Cycliophora), but support for both hypotheses was poor by Bayesian standards. Finally, most ML analyses recovered Platyzoa. However, support for Platyzoa decreased as OGs likely to contribute systematic error were excluded and most preliminary BI analyses recovered platyzoans as paraphyletic with strong support.