Background <p>Patterns of discordance between gene trees and the species trees they reside in are crucial to the coalescent vs. concatenation debate and may be key to resolving rapid radiations. However, errors in gene trees complicate the issue as topological errors can cause gene trees to appear erroneously discordant with the species tree. In this study, we evaluate the prevalence of discordance between gene trees and their species tree using an empirical dataset for a clade with a rapid radiation (Blaberidae). One key advance of our study is the use of complex, computationally intensive, selection-based codon models (FMutSel0 and SelAC) to identify the maximum likelihood gene tree. Our main hypothesis predicted that, if there are two competing topologies for a particular gene tree, then the one that is less discordant with the species tree will have less systematic error.</p> Results <p>Our experimental framework failed to show evidence for this, but only when discordance was measured in reference to a concatenation topology. In follow-up tests we see that the best candidate gene set yielded a coalescent species tree that was less discordant with gene trees.</p> Conclusions <p>We conclude from these tests that, although the frequency of discordance is on the low end of what is predicted by a range of modelling strategies, it is still extremely common overall and must be accounted for in order to achieve a biologically realistic outcome. These results allow us to support other relationships among blaberid cockroaches that were previously in flux as they now demonstrate molecular and morphological congruence. We suggest a few key improvements to the Blaberidae phylogeny, including identification of an anomaly zone spanning 10 backbone nodes and 6 additional nodes.</p>