Abstract. The genus Axelheibergella is established for cladocopid ostracods with well-developed, radially aligned septa between the outer lamella and the relatively wide, free-margin infold parts of the shell. Two deep-water species of the genus are described from the Holocene of the Alpha Ridge rise and Axel Heiberg slope, central Arctic Ocean (CAO). Two other species are present in the warmer, shallower waters of the Mediterranean region. Presumably the septa are designed to strengthen the free margin of the shell. The relationship of the camerae (interseptal chambers) to marginal pore canals in extant ostracods, including the Punciacopina, and to the marginal shell glands of cladocopids and halocypridid myodocopids is discussed. Cladocopid and podocopid (podocopine) shell ultrastructure is discussed, and new terms are defined. The septate frill and its function in the enigmatic Punciacopina are discussed in the light of recent discoveries of the radically different lifestyle of Manawa, and presumably of Puncia and Promanawa, from other non-punciacean ostracods. It is suggested that the frill of the Punciacopina is homologous to the ala of some cytheracean (cytherurid) podocopid ostracods. Two unnamed species of Puncia from the New Zealand Pleistocene are illustrated, and complement the discussion of septa and camerae in Axelheibergella.