A morphological cladistic analysis, consisting of 45 terminals and 58 characters was performed to evaluate the monophyly of the genus Paravima Caporiacco, 1951, and its relationship to other Leiosteninae. The analysis resulted in two most parsimonious trees, all recovering Paravima as monophyletic with the inclusion of two species formerly described in Avima Roewer, 1949, therefore, the following nomenclatural acts are herein proposed: Paravima plana (Goodnight & Goodnight, 1949) comb. nov., and Paravima quirozi (González-Sponga, 1981) comb. nov., Avima vigirima (Villarreal-M & Rodríguez-Manzanilla, 2003) is here considered as a junior subjective synonym of P. quirozi (González-Sponga, 1981) comb. nov., Paravima acanthoconus Villarreal-Manzanilla & DoNascimiento, 2005 is here considered as a junior subjective synonym of Paravima propespelunca González-Sponga, 1987, and Paravima flumencaurimarensis González-Sponga, 1987 is here considered as a junior subjective synonym of Paravima goodnightorum Caporiacco, 1951. Additionally, three new species are described: P. lokurasp. nov. (Tamá National Natural Park, Norte de Santander department) and P. magistrisp. nov. (Los Tunos Natural Reserve, Cundinamarca department), both from Colombia; and P. totorosp. nov. (Henri Pittier National Park, Aragua state) from Venezuela. Finally, an emended generic diagnosis, a key for all the species, and a distributional map are presented.