An important distinction lies between consciousness attributed to creatures, or subjects, (creature consciousness) and consciousness attributed to mental states (state consciousness). Most contemporary theories of consciousness aim at explaining what makes a mental state conscious, paying scant attention to the problem of creature consciousness. This attitude relies on a deeper, and generally overlooked, assumption that once an explanation of state consciousness is provided, one has also explained all the relevant features of creature consciousness. I call this the priority of state consciousness thesis (PSC). In this paper, I want to explore how the renewed centrality bestowed to phenomenology in contemporary discussions on consciousness challenges PSC and, consequently, the standard way of framing the problem of consciousness. More precisely, I examine PSC in light of a view about the structure of phenomenal character that is paradigmatic of the approach above. This is subjectivism about phenomenal character (SUBJ), according to which a mental state is conscious when it acquires the property of for-me-ness. I argue that PSC and SUBJ are incompatible because the latter implies that creature consciousness is explanatorily prior to state consciousness. Consequently, if SUBJ is true, then PSC is false, and what constitutes the problem of consciousness is primarily a problem of explaining (a kind of) creature consciousness. I conclude by defending my claim from a pair of possible objections and drawing some implications for the discussion of for-me-ness and the debate on the explanation of consciousness.