In addition to conceiving of such imaginary scenarios as those involving philosophical zombies, we may conceive of such things being conceived. Call these higher order conceptions ‘meta-conceptions’. Sorensen (2006) holds that one can entertain a meta-conception without thereby conceiving of the embedded lower-order conception. So it seems that I can meta-conceive possibilities which I cannot conceive. If this is correct, then meta-conceptions provide a counter-example to the claim that possibility entails conceivability. Moreover, some of Sorensen’s discussion suggests the following argument: if the conceivability of some proposition entails its possibility, then the meta-conceivability of some proposition entails its possibility; but we can meta-conceive impossibilities; so conceivability doesn’t entail possibility. In this paper, I’ll argue that one cannot entertain a meta-conception without thereby conceiving of the embedded lower-order conception. And so we can neither meta-conceive impossibilities nor meta-conceive possibilities of which we cannot thereby conceive.