Relations between frames and constructions must be made explicit in FrameNet-style linguistic resources such as Berkeley FrameNet (Fillmore & Baker, 2010, Fillmore, Lee-Goldman & Rhomieux, 2012), Japanese FrameNet (Ohara, 2013), and Swedish Constructicon (Lyngfelt et al., 2013). On the basis of analyses of Japanese constructions for the purpose of building a constructicon in the Japanese FrameNet project, this paper argues that constructions can be classified based on whether they evoke frames or not. By recognizing such a distinction among constructions, it becomes possible for FrameNet-style linguistic resources to have a proper division of labor between frame annotations and construction annotations. In addition to the three kinds of "meaningless" constructions which have been proposed already, this paper suggests there may be yet another subtype of constructions without meanings. Furthermore, the present paper adds support to the claim that there may be constructions without meanings (Fillmore, Lee-Goldman & Rhomieux, 2012) in a current debate concerning whether all constructions should be seen as meaning-bearing (Goldberg, 2006: 166-182).