Hinuq and Bezhta, two languages of the Tsezic sub-group of the Nakh-Daghestanian (East Caucasian) language family, have General noun modifying clause constructions (GNMCCs), which have also been noted in some other Nakh-Daghestanian languages. While readily acceptable and interpretable, GNMCCs that do not receive an interpretation with a coreferential element in the modifying clause are rare in natural discourse, certainly in comparison with Japanese, and the range of types also seems more restricted. We speculate that this is because Japanese by and large lacks sentential complement structures independent of GNMCCs, and moreover because Hinuq and Bezhta do not have highly frequent GNMCCs with light nouns, whose presence in Japanese serves to make GNMCCs a much more salient feature of discourse.