A subset of a finite additive abelian group G is a Z‐set if for all a ∈ G, na ∈ G for all n ∈ Z. The group G is called “Z‐good” if in every factorization G = A ⊕ B, where A and B are Z‐sets at least one factor is periodic. Otherwise G is called “Z‐bad.”The purpose of this paper is to investigate factorizations of finite ablian groups which arise from a variation of Sands′ method. A necessary condition is given for a factorization G = A ⊕ B, where A and B are Z‐sets, to be obtained by this variation. An example is provided to show that this condition is not sufficient. It is also shown that in general all factorizations G = A ⊕ B, where A and B are Z‐sets, of a “Z‐good” group do not arise from this variation of Sands′ method.