Abstract: According to the ‘objection from intimacy’, representationalism fails to make sense of the intimate, immediate nature of ‘inner awareness’, i.e. the special awareness that renders some of our mental states phenomenally conscious. The representationalist approach implies that one’s access to mental contents is mediated by representations, hence the contents could be misrepresented, which rules out intimacy. To address this objection, Levine, Hellie, Chalmers and others have construed inner awareness in terms of Russellian acquaintance, i.e. a direct, non-conceptual and substantive cognitive relation between a subject and her conscious contents. According to a common critique, however, the acquaintance-based model rules out naturalisability of consciousness since acquaintance is naturalistically suspect or even mysterious. I shall examine Sam Coleman’s attempt to dispel this worry by proposing a naturalistic – although non-representationalist – account of acquaintance. According to Coleman, we are acquainted with mental contents in having ‘quotational’ higher-order thoughts (QHOTs) about them, in which the contents are embedded and thus quoted. While Coleman’s model, as I will show, avoids the main pitfalls of representationalism, I will argue that it falls short of accounting for the intimacy of inner awareness. My argument is inspired by Levine’s critique of Balog’s related ‘quotational account’ of phenomenal concepts that, according to Levine, fails to explain the ‘cognitive presence’ of phenomenal states which some of our phenomenal concepts afford us. I’ll argue that a related objection applies to Coleman’s model, despite significant differences between the two accounts. I’ll conclude that the QHOT model isn’t suitable for modelling acquaintance and consider the prospects of a non-reductive approach to acquaintance.