In the several samples location problem, it is usually of interest to present estimates of treatment effects along with the test. The spatial Hodges–Lehmann estimators Δ^ij of the differences between treatments i and j are apparent companions to a multivariate Kruskal–Wallis test. However, these estimators generally fail to satisfy the property Δ^ij=Δ^ik+Δ^kj, making them incompatible with each other. In this paper we consider adjusted estimators possessing this property. A simulation study is carried out in order to study their finite sample efficiencies. Limiting distributions and efficiencies are presented as well.