What about Barrandeocerida

Flower, in Flower and Kummel, in A Classiification of the Nautiloidea, Journal of Paleontology Sept 1950, estalished the Barrandeocerida as a separate order, derived from the Tarphycerida. Barrandeocerids first appear in the Middle Ordovician, later than the Tarphycerida which first appear in the Lower Ordovician. Moreover Barrandeocerids have derived (evolved) characters, the principal one being thin connecting rings. So it makes, or made, sense to separate the two on an equal basis.

As recently as 1976, Flower in his paper of Ordovician Cephalopod Faunas, published by the Palaeontological Society ( Gr Br) separated the Barradeocerida from the Tarphycerida, deriving the former from the latter. This changed in 1984.

Flower, in Bodeiceras; a New Mohawkina Oxycone; ... Journal of Paleontology Nov. 1984, showed that the first two families of the Barrandeocerida, the Barradeoceratidae and Plectoceratidae are derived from different genera in the Tarphyceratidae, making the Barrandeocerida polyphyletic and therefore invalid, which according to Flower, should be abolished. Families that were included in the Barrandeocerida now belong in the Tarphycerida, which as a result has become greatly expanded. However Teichert, 1988, in has review paper on Main Features of Cephalopod Evolution in The Mollusca Vol 12, Academic Press, retained the Barrandeocerida as a distiinct group, but as a suborder of the Tarphycerida, the Barrandeocerina. The other suborder of course being the Tarphycerina.

Flower's claim that the Barrandeoceratidae are derived from Centrotarphyceras and that the Plectoceratidae are derived from Campbelloceras is not stated with clear evidence, but is left for the reader to simply accept, or reject. For this reason the claim that the Barrandeocerida (sensu Flower 1950) is polyphyletic can not be taken as an absolute. It is obvious however that barrandeocerids form a group that evolved from earlier tarphycerids and might just as well be included as a suborder pending further evidence of separate origins for the Barradeoceratidae and Plectoceratidae.