I examine the conditions which hypotheses must satisfy if they are to be used to raise significant sceptical challenges. I argue that sceptical hypotheses do not have to be logically, metaphysically or epistemically possible: they need only to depict scenarios subjectively indistinguishable from the actual world and to show how subjects can believe what they do while not having knowledge. I also argue that sceptical challenges can be raised against a priori beliefs, even if those beliefs are necessarily true. I hope to broaden our conception of the legitimate kinds of sceptical challenges which can be raised.