Inequalities in health and health care are caused by different factors. Measuring "unfair" inequalities implies that a distinction is introduced between causal variables leading to ethically legitimate inequalities and causal variables leading to ethically illegitimate inequalities. An example of the former could be life-style choices, an example of the latter is social background. We show how to derive measures of unfair inequalities in health and in health care delivery from a structural model of health care and health production: "direct unfairness", linked to the variations in medical expenditures and health in the hypothetical distribution in which all legitimate sources of variation are kept constant; "fairness gap", linked to the differences between the actual distribution and the hypothetical distribution in which all illegitimate sources of variation have been removed. These two approaches are related to the theory of fair allocation. In general they lead to different results. We propose to analyse the resulting distributions with the traditional apparatus of Lorenz curves and inequality measures. We compare our proposal to the more common approach using concentration curves and analyse the relationship with the methods of direct and indirect standardization. We discuss how inequalities in health care can be integrated in an overall evaluation of social inequality.