Measuring and monitoring socioeconomic health inequalities are critical for understanding the impact of policy decisions. However, the measurement of health inequality is far from value neutral, and one can easily present the measure that best supports one's chosen conclusion or selectively exclude measures. Improving people's understanding of the often implicit value judgments is therefore important to reduce the risk that researchers mislead or policymakers are misled. While the choice between relative and absolute inequality is already value laden, further complexities arise when, as is often the case, health variables have both a lower and upper bound, and thus can be expressed in terms of either attainments or shortfalls, such as for mortality/survival. We bring together the recent parallel discussions from epidemiology and health economics regarding health inequality measurement and provide a deeper understanding of the different value judgments within absolute and relative measures expressed both in attainments and shortfalls, by graphically illustrating both hypothetical and real examples. We show that relative measures in terms of attainments and shortfalls have distinct value judgments, highlighting that for health variables with two bounds the choice is no longer only between an absolute and a relative measure but between an absolute, an attainment- relative and a shortfall-relative one. We illustrate how these three value judgments can be combined onto a single graph which shows the rankings according to all three measures, and illustrates how the three measures provide ethical benchmarks against which to judge the difference in inequality between populations.