I characterize those abstract choice problems for which the satisfaction of the weak axiom of revealed preference suffices for the strong rationalizability of any choice correspondence. The condition is non-monotone, and is satisfied by both very small and very large budget collections. I additionally provide a notion of local integrability for an abstract choice correspondence, and prove an ordinal variant of the Hurwicz-Uzawa integrability theorem that holds in the full generality of the abstract choice model. I fully characterize how complete the domain of a choice correspondence must be for the weak axiom and local integrability to jointly guarantee strong rationalizability.