Objective: In the past decade, much has been written about the hard problem of consciousness in the philosophy of mind. However, a separate hard problem faces the scientific study of consciousness. The problem arises when distinguishing the neural correlates of consciousness (NCC) and the neural constitution of consciousness. Here, I explain this correlation/constitution distinction and the problem it poses for a science of phenomenal consciousness. I also discuss potential objections to the problem, outline further hard problems in the scientific study of phenomenal consciousness and consider the ontological implications of these epistemological issues. Methods: Scientific and philosophic analysis and discussion are presented. Results: The correlation/constitution distinction does indeed present a hard problem in the scientific study of phenomenal consciousness. Refinement of the NCC acronym is proposed so that this distinction may at least be acknowledged in the literature. Furthermore, in addition to the problem posed by this distinction and to the hard problem , the scientific study of phenomenal consciousness also faces several other hard problems. Conclusion: In light of the multiple hard problems, it is concluded that scientists and philosophers of consciousness ought to (i) address, analyze and discuss the problems in the hope of discovering their solution or dissolution and (ii) consider the implications of some or all of them being intractable. With respect to the latter, it is argued that ultimate epistemic limits in the study of phenomenal consciousness pose no threat to physicalist or materialist ontologies but do inform our understanding of consciousness and its place in nature.