A clear distinction may be drawn between the perpendicular architecture of the feeding apparatus of ozarkodinid, prioniodontid and prioniodinid conodonts, in which the P elements are situated at a high angle to the M and S elements, and the parallel architecture of panderodontid and other coniform apparatuses, where two suites of coniform elements lie parallel to each other and oppose across the midline. The quest for homologies between the two architectures has been fraught with difficulty, at least in part because of the paucity of natural assemblages of coniform taxa. A diagenetically fused apparatus of Cordylodns lindstroini elements is here described which is made up of one rounded and two compressed element morphotypes. One of the compressed elements is bowed and asymmetrical and the other is unbowed and more symmetrical. These compressed elements are considered to be homologous with those of panderodontid apparatuses and would have lain at the caudal end of the parallel arrays, with the more symmetrical morphotypes located rostrally to the asymmetrical ones. The bowed and unbowed compressed elements of Cordylodns thus correspond, respectively, to the pt and pf positions of panderodontid apparatuses. In addition, the presence of symmetry transition within the rounded elements of Cordylodns, but not the compressed morphotypes, enables correlation of these with the S and M element locations of ozarkodinid apparatuses. By extension, the compressed elements must be homologues of the P elements. Specifically, the asymmetrical pt morphotype is homologous with the P1 of ozarkodinids and the more symmetrical and rostral pf morphotype is homologous with the P2 position. However, because of uncertainties over the nature of topological transformation of the rostral element array (the "rounded" or "costate" suites), it is not possible to recognize specific homologies between these elements and the M and S elements of ozarkodinids. Morphologic differentiation of P from M and S element suites thus preceded the topological transformation from parallel to perpendicular apparatus architectures.