Nucleotide substitution models used in molecular phylogenetics do not account for nucleotide sequences evolving under selection, yet selection is rarely tested for. If non-neutral markers violate these models (i.e. non-independence of sites), it is expected that their reconstructed topologies be incongruent with those inferred from neutral ones and conclusions made from those phylogenies should be reexamined. Using rhodopsin as a phylogenetic marker has recently been called into question for exactly this reason. Rhodopsin is assumed to have evolved under strong positive selection for organisms that inhabit similar aquatic environments, making it unsuitable for the phylogenetics of aquatic organisms, but it is unclear what the effects of non-neutrality on phylogeny estimation are. To evaluate potential incongruence of neutral versus non-neutral markers, and the notion that rhodopsin should not be used in the molecular phylogenetics of fishes, a molecular dataset of 78 acanthomorph taxa and sequences from four nuclear, protein coding loci (including rhodopsin), were examined. Only one marker was found to be neutral while the remaining tests, for all other loci, rejected the null hypothesis of neutrality. To evaluate the possible effect(s) of positively versus negatively selected sites, the three non-neutral markers were analyzed to determine the presence of positively and negatively selected codons. To determine congruence in topology among ML trees inferred by individual neutral and non-neutral markers, as well as the combined (concatenated) dataset, tree, comparisons of distances among trees and hypothesis (topology) testing were carried out. Results of the tree distance metrics and topology testing support the notion that neutrality alone does not determine congruence in topology, and those data that are inferred to have evolved under selection should not necessarily be excluded. In addition, the number of sites inferred to have evolved under positive selection does not predict congruence with other markers or the topology inferred with the concatenated dataset.