In this paper I address the question of whether the fact that our colour experiences have a finer-grained content than our ordinary colour concepts allow us to represent should be taken as a threat to theories of the conceptual content of experience. In particular, I consider and criticise McDowell's response to that argument and propose a possible development of it. As a consequence, I claim that the role of the argument from the finer-grained content of experience has to be redefined. In particular, I acknowledge that this problem is helpful in order to bring to the fore the issue of the proper characterisation of the constraints upon the possession conditions of perceptual demonstrative concepts. Yet, I contend that, in light of the foregoing discussion, it is neutral with respect to the dispute between conceptual and non-conceptual theorists. For that dispute hinges on whether it is possible to have experiences with a certain content independently of having the concepts, which are needed for its canonical specification and not on whether those experiences are conceptualisable in all their finesse of grain.