<p>Zombies are non-conscious physical duplicates of conscious physical entities. It has been argued that the conceivability of zombies supports their (metaphysical) possibility (Chalmers in The conscious mind, Oxford University Press, Oxford, 1996; in The two-dimensional argument against materialism, pp 414–201, 2010a, in The character of consciousness, Oxford University Press, Oxford, 2010b). This is important because if zombies are possible then physicalism is false. The jury has been out for decades on the possibility of zombies. This essay argues in a new way that either zombies are inconceivable or conceivability isn’t a valid guide to possibility. Either way, the threat to physicalism from zombies is neutralized. The central idea, which is developed by examining the mereological argument against zombies (Giberman in Mind 124: 121–146, 2015), is based on the premise that, for arbitrary conscious particular x, it is conceivable that consciousness facts about x are entirely independent of mereological-cum-spatiotemporal complexity facts about x. This premise is required for the conceivability of zombies, lest room be left for consciousness to be fixed by exact mereological-cum-spatiotemporal resemblance to a conscious entity. Yet the premise also clears the way for the conceivability of a version of panpsychism modally potent enough for its conceivability either to render zombies inconceivable or to undermine the conceivability-possibility link.</p>