Applying morphological operators to colour images requires that the colour vectors can be ordered. In this paper we propose an alternative to traditional lexicographic ordering methods by replacing the hue component with a new component named anti-saturation, which is the distance from the given colour vector to the boundary of the colour cube. While anti-saturation does not permit a total ordering, as does the hue angle, it both varies smoothly with hue angle and does not contain any discontinuities, making it a plausible candidate for a third level of lexicographic ordering instead of hue-angle.