Binary possibilistic utility unifies two previously proposed qualitative decision models: optimistic and pessimistic utilities. All these decision models have been axiomatized in a von Neumann-Morgenstern setting. These axiomatizations have shown the formal similarity of these qualitative utilities and expected utility. Unfortunately in this framework, the representation of uncertainty has to be clearly assumed to be given. In a more general setting, without this restriction, optimistic and pessimistic utilities have been axiomatized à la Savage. This paper proposes a study of the axiomatics of binary possibilistic utility in a Savagean framework.