This paper contributes to the current debate about radical scepticism and the structure of warrant. After a presentation of the standard version of the radical sceptic’s challenge, both in its barest and its more refined form, three anti-sceptical responses, and their respective commitments, are being identified: the Dogmatist response, the Conservativist response and the Dretskean response. It is then argued that both the Dretskean and the Conservativist are right that the anti-sceptical hypothesis cannot inherit any perceptual warrants from ordinary propositions about the environment—and so the Dogmatist response founders. However, if this is so Epistemic Closure lacks any clear rationale. There is therefore good reason to agree with both the Dretskean and the Dogmatist that perceptual warrants for ordinary propositions about the environment are enough in order for those propositions to enjoy a positive epistemic status—and so the Conservativist response founders. However, the Conservativist is nonetheless right that a warrant for the anti-sceptical hypothesis is needed. For contrary to what much of the recent literature suggests, the radical sceptic need not appeal to Epistemic Closure in order to cast doubt on the legitimacy of our beliefs in ordinary propositions about the environment: there is a Pyrrhonian version of scepticism that, though equally radical, is consistent with failure of Epistemic Closure. For this reason, the Dretskean response is insufficient to answer scepticism.