The annotation guidelines for Universal Dependencies (UD) stipulate that the basic units of dependency annotation are syntactic words, but it is not clear what are syntactic words in Japanese. Departing from the long tradition of using phrasal units called bunsetsu for dependency parsing, the current UD Japanese treebanks adopt the Short Unit Words. However, we argue that they are not syntactic word as specified by the annotation guidelines. Although we find non-mainstream attempts to linguistically define Japanese words, such definitions have never been applied to corpus annotation. We discuss the costs and benefits of adopting the rather unfamiliar criteria.