We investigate the basic monotonicity properties of least-distance (in)efficiency measures on the class of non-convex FDH (free disposable hull) technologies. We show that any known FDH least-distance measure violates strong monotonicity over the strongly (Pareto-Koopmans) efficient frontier. Taking this result into account, we develop a new class of FDH least-distance measures that satisfy strong monotonicity and show that the developed (in)efficiency measurement framework has a natural profit interpretation.