We address the question of the measurement of health achievement and inequality in the context of variables exhibiting an inverted-U relation with health and well-being. The chosen approach is to measure separately achievement and inequality in the health increasing range of the variable, from a lower survival bound a to an optimum value m, and in the health decreasing range from m to an upper survival bound b. Because in the health decreasing range, the equally distributed equivalent value associated with a distribution is decreasing in progressive transfers, the paper introduces appropriate relative and absolute achievement and inequality indices to be used for variables exhibiting a negative association with well-being. We then discuss questions pertaining to consistent measurement across health attainments and shortfalls, as well as the ordering of distributions exhibiting an inverted-U relation with well-being. An illustration of the methodology is provided using a group of five Arab countries.