Since the 1960s, huge progress has been made in reconstructing the multielement skeletons of conodont species and developing a biologically defensible taxonomy. Nevertheless, a widespread prejudice remains that certain parts of the conodont skeleton, particularly the P-1 elements, are more informative than others with regard to taxonomy and evolutionary relationships. Here, we test these views. A new partial multielement reconstruction of the skeleton of the biostratigraphically significant conodont originally described as Gnathodus commutatus homopunctatus allows us to conduct a cladistic test of the alternative hypotheses of phylogenetic placement of this species. Our analysis also provides the first test of the hypothesis that Lochriea - species of which are markers for global correlation - is monophyletic and tests hypotheses concerning the origins of the genus. Our results demonstrate that homopunctatus is a species of Lochriea and that the genus is monophyletic. The widely held view that Lochriea arose from a species of Bispathodus is not supported. Our results show that it is difficult to predict a priori which parts of the conodont skeleton carry phylogenetic signal, and provide strong support for the hypothesis that similarity in the morphology of conodont P-1 elements alone is not a reliable guide to relationships and taxonomic groupings of conodont species. This is because P-1 elements with similar morphologies are convergently acquired in multiple conodont clades, because reliance on the characters of only one of the six or seven morphologically distinct elements of the conodont skeleton ignores phylogenetically significant data and because P-1 elements can lack characters that might seem to be diagnostic of a genus. Conodonts are no different to other organisms: ignoring data that have the potential to be phylogenetically informative is unlikely to produce the most reliable hypotheses of evolutionary relationships. We suggest that other biostratigraphically significant hypotheses of relationship between conodont taxa that are based on P-1 elements alone should be subject to cladistic testing.