A critique of attributer contextualist treatments of the problem of radical scepticism is offered. It is argued that while such proposals, standardly conceived, gain some purchase against the closure-based formulation of this problem, they run aground when applied to the logically distinct underdetermination-based formulation. A specific kind of attributer contextualism—rational support contextualism—is then explored. This is better placed to deal with underdetermination-based radical scepticism via its endorsement of ascriptions of factive rational support in everyday contexts of epistemic appraisal. But such a proposal is faced with a dialectical impasse with regard to the competing epistemological disjunctivist response to radical scepticism. While the former has dialectical advantages over the latter with regard to closure-based radical scepticism, the latter has the dialectical upper-hand when it comes to underdetermination-based radical scepticism. It is claimed that the way to resolve this issue—and thereby to understand that we should not expect a unified treatment of these two formulations of the sceptical problem, much less one that is cast along contextualist lines—is to recognise how these two formulations reflect distinct sources of scepticism.