A number of theories of consciousness define consciousness by the folk-intuition that consciousness is somehow aware of, or "given' to itself. I attempt to undermine this intuition on phenomenological, conceptual and psychological grounds. An alternative, first-order theory of consciousness, however, faces the task of explaining the possibility of self-awareness for consciousness, as well as the everyday intuition supporting it. I propose that another, weaker kind of givenness, "givenness as availability', is up to both of these tasks, and is therefore sufficient and suitable for first-order theories of consciousness.