In this paper we reconstruct the phylogeny of a clade of pachypleurosaurs (Reptilia: Sauropterygia) occurring in Triassic-age deposits in the Monte San Giorgio region, Switzerland. We also present the phylogeny of this clade as a case study for two paradigms of phylogeny reconstruction: cladistics and phenetic/stratigraphic methods. While this dichotomy is not held rigidly by all workers, its advancement by cladists leads us to retain it initially for rhetorical purposes. We review the philosophical bases of species, species concepts, and speciation, as well as cladograms and phylogenies, before introducing the experimental system. Data are presented from cladistic analyses, phenetic analyses, and stratigraphic information. Phylogeny of the clade is interpreted from both paradigms, and the interpretations are found to be inconsistent. Resolution of the phylogeny rests on the emphasis of one type of data over another. An interpretation of cladogenesis within the genus Neusticosaurus entails rejection of suggestive phenetic and stratigraphic data, whereas an anagenetic interpretation entails reversal of autapomorphies in ancestral taxa. Anagenesis is deemed to be the more probable interpretation, based on the strength of the stratigraphic and phenetic data relative to the character data. Implications of the test case results for phylogeny reconstruction in general are discussed, ending with a call for pluralism in approach.