The concentration index is widely used to measure income-related inequality in health. No insight exists, however, whether the concentration index connects with people’s preferences about distributions of income and health and whether a reduction in the concentration index reflects an increase in social welfare. We explored this question by testing the central assumption underlying the concentration index and found that it was systematically violated. We also tested the validity of alternative health inequality measures that have been proposed in the literature. Our data showed that decreases in the spread of income and health were considered socially desirable, but decreases in the correlation between income and health not necessarily. Support for a condition implying that the inequality in the distribution of income and in the distribution of health can be considered separately was mixed.