For the past 35 years, the Cambrian fossil Pikaia gracilens was widely interpreted as a typical basal chordate based on short descriptions by Conway Morris. Recently, Conway Morris and Caron (CMC) (2012, Biol Rev 87:480-512) described Pikaia extensively, as a basis for new ideas about deuterostome evolution. This new Pikaia has characters with no clear homologues in other animals, so they could be phylogenetically uninformative autapomorphies. These characters include a dorsal organ, posterior ventral area, posterior fusiform structure, and anterior dorsal unit. Yet CMC interpret most of the unusual characters as primitive for chordates, thereby interpreting Pikaia as an even more convincing stem chordate than before. Moreover, they claim that segment (myomere) shape is a reliable guide for defining a chordate and even for assigning animals to their correct place in deuterostome phylogeny. By defining sigmoidal segments as a basal chordate character, they situate Pikaia at the base of the chordates and banish fossil yunnanozoans (which have straight segments) to a position deep within the deuterostomes. In addition, they consider amphioxus, with its conspicuously chevron-shaped segments, to be so highly derived that it is of little use for reconstructing the first chordates. We question their overemphasis on the phylogenetic value of segment shape and their marginalizing of amphioxus. We deduce that Pikaia, not amphioxus, is specialized. We performed a cladistic analysis that showed the character interpretations of CMC are consistent with their wide-ranging evolutionary scenario, but that these interpretations leave unresolved the position of Pikaia within chordates.