Although the naupliar and cypridiform stages of the enigmatic y-larvae of Facetotecta have been found in the marine plankton worldwide, they still represent the last significant group of crustaceans for which the adult forms are still unknown. From a number of y-cyprids representing different taxa from different locations, we employ scanning electron microscopy to describe fine morphological details of all external structures of this unique larval form. We document different segmentation patterns of the abdomen and presence/absence of the labrum and structural differences in the antennules, labrum, paraocular process, thoracopods, and telson lend support for the erection of several new genera as opposed to the single Hansenocaris. The data presented here emphasize the morphological limits of the genus Hansenocaris and the “bauplan” of cyprydiform larvae of Facetotecta. Although the optimum pathway is a joint analysis of both molecular and morphological characters, we use the morphological characters of y-cyprids to align them cladistically and determine the limits of the genus Hansenocaris s.s. and describe common characters for all y-cyprids including six pairs of the lattice organs instead five pairs considered as a ground pattern for all Thecostraca. We also determine plesiomorphic and apomorphic characters of all known y-cyprids and separate them from other thecostracan cypridiform larvae.