Debate over whether phonaesthemes are part of morphology has been long and inconclusive. We contend that this is because the properties that characterise individual phonaesthemes and those that characterise individual morphological units are neither sufficiently disjunct nor sufficiently overlapping to furnish a clear answer, unless resort is made to relatively aprioristic exclusions from the set of ‘relevant’ data, in which case the answers follow directly and uninterestingly from initial assumptions. In response, we pose the question: ‘According to what criteria, if any, do phonaesthemes distinguish themselves from non-phonaesthemic, stem-building elements?’, and apply the methods of Canonical Typology to seek answers. Surveying the literature, we formulate seven canonical criteria, identifying individual phonaesthemes which are more, or less, canonical according to each. We next apply the same criteria to assess non-phonaesthemic stem-building elements. The result is that just one criterion emerges which clearly differentiates the two sets of phenomena, namely the canonical accompaniment of phonaesthemes by non-recurrent residues, and this finding is not predetermined by our assumptions. From the viewpoint of morphological theory more broadly, we assume that any viable theory must find a place for lexical stems which are composed of a recurring, sound-meaning pairing plus a non-recurrent residue. Most phonaesthemes will occur in such stems. Consequently, theoretically interesting questions can then be asked about this entire class of lexical stems, including but not limited to its phonaesthemic members. Whether they are ‘part of morphology’ or not, phonaesthemes can contribute coherently to the development of morphological theory.