A unification algorithm is said to be minimal for a unication problem if it generates exactly a (minimal) complete set of most-general unifiers, without instances, and without repetitions. The aim of this paper is to present a combinatorial minimality study for a signicant collection of sample problems that can be used as benchmarks for testing any set-unification algorithm. Based on this combinatorial study, a new Set-Unification Algorithm (named SUA) is also described and proved to be minimal for all the analyzed problems. Furthermore, an existing naive set-unification algorithm has also been tested to show its bad behavior for most of the sample problems.