The diversity of 'accessory orifices' (sutural pores, cothurnopores, lamellipores) in cornute stylophorans is reviewed, based on detailed examination of both previously described and new material, to discuss their similarities and differences with other deuterostome respiratory structures. The orifices present in the most basal taxa (e.g. Ceratocystis and Nevadaecystis) are morphologically identical to the sutural pores of many other Cambrian echinoderms, therefore ruling out previous interpretations of these structures as multiple mouths, gonopores, and gill slits. Cothurnopores correspond to highly specialized covered sutural pores, each delimited by a pair of U-shaped plates. The large 'accessory orifices' of Phyllocystis crassimarginata, along with the morphologically identical but smaller ones observed in cothurnopores, are here designated as pustulipores; in life, they probably housed soft, papulae-like exothecal respiratory structures. Proto-lamellate organs correspond to dense aggregations of cothurnopores that lack pustulipores. Lamellate organs are reinterpreted as highly folded structures, functionally analogous to pectinirhombs, composed of numerous, sutured lamellae, each consisting of a pair of tightly compressed U-shaped plates. No evidence supports the presence of a flap in cothurnopores, nor slit-like openings (lamellipores) in lamellate organs. The genus Thoralicystis is here reinstated as valid, and Proscotiaecystis is considered a junior synonym.