This paper focuses on decisive belief revision operators, i.e. operators leading to totally informed situations. Such situations can be represented in the Katsuno-Mendelzon (KM) revision framework by a complete propositional formula, from which either any formula or its negation can be entailed. From a semantic point of view, this kind of operator leads to a single, most plausible interpretation. Despite their prevalence in decision theory, this class of operators has not been previously studied in the context of the KM revision framework. We propose in this paper to characterize decisive operators by a set of postulates. We also provide a representation theorem leading to total orders on interpretations. Finally, we exhibit a concrete operator family satisfying this new set of postulates by combining KM revision operators with tie-breaking functions.