solanum medians is a widely distributed species of wild potato (solanum sect. petota), growing along the coastal lomas and up the western slopes of the Andes Mountains from central Peru and northern Chile, from 200–3800 m elevation. Fertile diploid and sterile triploid cytotypes are common, are believed to be associated with morphological variants, and are formally named as subspecies. A morphometric study based on principal components and canonical discriminate analyses of characters obtained from herbarium specimens tests the circumscription of these subspecies and other currently recognized species that are very similar to S. medians. The results show so much overlap of these taxa that it is impractical to use morphology to define species or to provide reliable keys or identifications. We synonymize ten names under S. medians: S. medians var. angustifoliolum, S. medians var. majorifrons subvar. majorifrons, S. medians var. majorifrons subvar. protohypoleucum, S. medians var. autumnale, S. sandemannii, S. tacnaense, S. weberbaueri var. decurrentialatum, S. tacnaense f. decurrentialatum, S. weberbaueri, S. weberbaueri var. poscoanum. We also treat S. neoweberbaueri as a closely related species to S. medians. We consider the synonymy in S. medians to be part of a much larger need for reduction of names in sect. petota.