Wiwaxia corrugata and the indisputable polychaetes of the Middle Cambrian Burgess Shale, particularly Canadia spinosa, have figured prominently in recent hypotheses about the early evolution of polychaete annelids. Based on similarities between the sclerites of Wiwaxia and the notochaetae of Canadia with the broad notochaetae (paleae) of Recent chrysopetalid polychaetes, these two fossil taxa have been variously treated as closely related to the most highly derived stem forms of the polychaete (and annelid) crown group or as members of a specific, Recent subgroup within Polychaeta, the order Phyllodocida. Chrysopetalidae is a member of Phyllodocida, which is part of the major polychaete clade Aciculata; the latter two taxa are distinguished by four and six well defined autapomorphic characters, respectively. The best preserved or otherwise appropriate fossils of Wiwaxia corrugata, Canadia spinosa and the other polychaetes of the Burgess Shale have been studied in detail in order to determine whether they possess any characters that could support the homology of wiwaxiid sclerites, canadiid notochaetae and chrysopetalid paleae. Most of these fossil taxa have significant autapomorphies but the specific characters of the Aciculata and Phyllodocida are entirely absent. It is demonstrated that constraining cladograms in such a manner that wiwaxiid sclerites, canadiid notochaetae and chrysopetalid paleae are homologous leads to results that are markedly unparsimonious. Furthermore, Canadia and the other polychaetes of the Burgess Shale cannot be referred to any extant subgroup within the Polychaeta and cannot be used to polarize character evolution within the annelid crown group. Apart from its dubious sclerites, Wiwaxia has no characters that could indicate any close relationship with Polychaeta or Annelida.