Here I address the “phenomenal concept strategy” for addressing anti-materialist intuitions, such as the explanatory gap, by appealing to the special nature of phenomenal concepts. I look in depth at several proposals, including John Perry’s influential presentation in Knowledge, Possibility, and Consciousness, and argue that they all fail in meeting what I call the “materialist constraint”, which is the principle that no property or relation that is not realizable in physical properties or relations be appealed to in the account. I conclude that some relation such as acquaintance must be invoked to explain our first-person access to conscience experience, and that currently no materialist model for such a relation exists.