Nick Bostrom’s ‘Simulation Argument’ purports to show that, unless we are confident that advanced ‘posthuman’ civilizations are either extremely rare or extremely rarely interested in running simulations of their own ancestors, we should assign significant credence to the hypothesis that we are simulated. I argue that Bostrom does not succeed in grounding this constraint on credence. I first show that the Simulation Argument requires a curious form of selective scepticism, for it presupposes that we possess good evidence for claims about the physical limits of computation and yet lack good evidence for claims about our own physical constitution. I then show that two ways of modifying the argument so as to remove the need for this presupposition fail to preserve the original conclusion. Finally, I argue that, while there are unusual circumstances in which Bostrom’s selective scepticism might be reasonable, we do not currently find ourselves in such circumstances. There is no good reason to uphold the selective scepticism the Simulation Argument presupposes. There is thus no good reason to believe its conclusion.