Most specimens of carnivorous sponges (Demospongiae, Poecilosclerida, Cladorhizidae) collected in the deep Pacific are usually found to be undescribed taxa. New Zealand’s EEZ, containing Kermadec Trench and Volcanic Arc to the north, Chatham Rise to the southeast, and parts of Macquarie Ridge to the southwest of New Zealand, as well as parts of Australia’s EEZ surrounding Macquarie Island, on Macquarie Ridge, have produced high numbers of new species and possibly new genera, and these are presently being described. In this work, we describe three new species of Cladorhizidae, each remarkable for the ‘exceptions to the rule’ that they represent. Abyssocladia carcharias sp. nov., from Monowai Seamount on the Kermadec Volcanic Arc, has the shape of a pedunculate disc with radiating filaments, and is characterized by three types of unique multidentate isochelae. Asbestopluma (Asbestopluma) anisoplacochela sp. nov., from the southern most end of the Three Kings Ridge, is erect and cylindrical with lateral expansions. In addition to the usual Asbestopluma microscleres, this species displays a new form of microsclere, termed ‘anisoplacochelae’. These unprecedented microscleres bear a plate-like central tooth similar to that of the placochelae of Guitarridae, but the ends are dissimilar in shape and dimensions. Asbestopluma (Asbestopluma) desmophora sp. nov., from Cavalli Seamounts off the north east coast of New Zealand, Hikurangi Plateau to the east of the North Island, and the Chatham Rise extending east from the South Island (all New Zealand EEZ), and on Macquarie Ridge (Australia EEZ), is an erect dichotomously branching sponge, that has desma megascleres densely packed into the enlarged base of attachment. Implications for the phylogeny of these three unusual species are considered.