We present a procedure for computing the sceptical “deal semantics” for argumentation in assumption-based frameworks. This semantics was first proposed for logic programming in [1], extending the well-founded semantics. The proof procedure is defined by means of a form of dispute derivations, obtained by modifying the dispute derivations given in [2] for computing credulous admissible argumentation. The new dispute derivations are sound for the “ideal semantics” in all cases where the dispute derivations of [2] are complete for admissible argumentation. We prove that this is the case for the special kind of assumption-based frameworks with a finite underlying language and with the property of being “p-acyclic”.