According to the standard argument from targetless higher‐order representations, the possibility of such representations presents a dilemma for higher‐order theorists. In this article I argue that there are two theoretically well‐motivated replies to the standard argument. Consequently, the standard argument against higher‐order theories fails. I then go on to argue that while certain versions of higher‐order theory can adequately respond to the standard argument, they both, nevertheless, fail to explain the fineness‐of‐grain that phenomenally conscious experience appears to have.