Epistemologists have differed in their assessments of what it is in virtue of which skeptical hypotheses succeed in raising doubts. It is widely thought that skeptical hypotheses must satisfy some sort of possibility constraint and that only putative knowledge of contingent and a posteriori propositions is vulnerable to skeptical challenge. These putative constraints have been disputed by a number of epistemologists advocating what we may call “the non-standard view.” My main concern in this paper is to challenge this view by identifying a general recipe by means of which its proponents generate skeptical scenarios. I will argue that many of the skeptical arguments that are founded on these scenarios undermine at most second-order knowledge and that to that extent the non-standard view’s rejection of the standard constraints on skeptical hypotheses is problematic. It will be argued that, pace the non-standard view, only in their error-inducing capacities can skeptical hypotheses challenge first-order knowledge. I will also dispute the non-standard view’s claim that its skeptical arguments bring to light a neglected form of radical skepticism, namely, “a priori skepticism.” I conclude by contending that the non-standard view’s account of how skeptical hypotheses can raise legitimate doubt actually rides piggyback on the standard ways of challenging the possibility of knowledge.