Based on study of herbarium specimens of Cyperus sect. Incurvi Kük., three species are described from the lowlands of N South America and Mesoamerica: C. conservator-davidii G. C. Tucker is a new species occurring in several countries and is morphologically similar to C. simplex Kunth; C. lacustris Schrad. ex Nees is an overlooked species that has been confused with C. miliifolius Poepp. & Kunth; C. altsonii Kük. and C. hoppiifolius Uittien pertain to the same species, for which the former is the earlier name. An identification key is provided for all species of C. sect. Incurvi occurring in the New World.