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.