This paper reviews and extends the theory of ethical inequality indices. It presents a novel axiom (strict separability of social welfare orderings in rank-ordered subspaces). This axiom allows to provide joint characterizations of the most important inequality measures (Atkinson family, Kolm-Pollak family and Generalized Ginis) and of some new more general classes of indices. The whole derivation is based on weak assumptions. In an ordinal framework only continuity of the underlying ordering is required and no cardinal properties are employed.