It appears that consciousness science is progressing soundly, in particular in its search for the neural correlates of consciousness. There are two main approaches to this search, one is content-based (focusing on the contrast between conscious perception of, e.g., faces vs. houses), the other is state-based (focusing on overall conscious states, e.g., the contrast between dreamless sleep vs. the awake state). Methodological and conceptual considerations of a number of concrete studies show that both approaches are problematic: the content-based approach seems to set aside crucial aspects of consciousness; and the state-based approach seems over-inclusive in a way that is hard to rectify without losing sight of the crucial conscious-unconscious contrast. Consequently, the search for the neural correlates of consciousness is in need of new experimental paradigms.