In many problem domains, solutions take the form of unordered sets. We present the Set-Enumerations (SE)-tree - a vehicle for representing sets and/or enumerating them in a best-first fashion. We demonstrate its usefulness as the basis for a unifying search-based framework for domains where minimal (maximal) elements of a power set are targeted, where minimal (maximal) partial instantiations of a set of variables are sought, or where a composite decision is not dependent on the order in which its primitive component-decisions are taken. Particular instantiations of SE-tree-based algorithms for some AI problem domains are used to demonstrate the general features of the approach. These algorithms are compared theoretically and empirically with current algorithms.