The circumscription of the five to eight species of Luffa, as well as their correct names, have long been problematic. Experts on the genus, most recently C. Heiser and C. Jeffrey, have disagreed on the number of species in the New World and the application of the name L. operculata, which in turn affected the names L. quinquefida and L. sepium. Heiser used classic biosystematic methods, including experimental crossing, to infer species boundaries, but neither researcher had today's option of using DNA sequences for this purpose. We sequenced 51 accessions of Luffa, representing the geographic range of the genus and as much as possible topotypical or type material. Phylogenies from four non-coding plastid regions and the nuclear ribosomal DNA spacer region show that eight clades of specimens have geographic-morphological coherence. Heiser's view that Luffa has three species in the New World is supported, and there are four species in tropical and subtropical Asia. Australia has an endemic species, differing from the Indian species with which it had long been lumped. Our vouchered ITS and plastid sequences from throughout species' ranges are available in GenBank and can serve to identify Luffa material similar to standard DNA barcoding regions. We also provide new arguments for Heiser's application of the name L. operculata to a South American species, countering Jeffrey's arguments in favor of its use for a Central American species.