The calcichordate scenario of Jefferies and colleagues purports to explain the origin and early evolution of the phyla Echinodermata and Chordata. Calcichordate proponents have argued that echinoderms are the sister group of the chordates and urochordates are the sister group of the craniates. These phylogenetic hypotheses, which differ from the traditional groupings, are derived primarily from morphological interpretations of carpoids (solutes, cornutes, and mitrates), an enigmatic fossil group usually held to be primitive stem‐group echinoderms. Although the scenario has received only limited support, it has yet to be falsified. The difficulty with falsifying the calcichordate scenario is proving that the morphological interpretations, for example, that carpoids possessed notochords, dorsal hollow nerve cords, and other typical chordate or craniate characters, are incorrect. Here, rather than argue over the interpretation of fossils, the phylogenetic hypotheses embedded within the scenario are tested. It is found that the calcichordate scenario fails such a test, even if both the Recent and fossils forms are coded according to the calcichordate scenario. It is argued that: (1) the erection of scenarios must follow the construction of a cladogram; and (2) fossils are unable to dictate the relationships among phyla. □Calcichordate scenario, Carpoidea, Deuterostomia, Echinodermata, Chordata, phylogeny, cladist