When incorporating differences in household characteristics, the choice of equivalence scale can affect the ranking of income distributions. An alternative approach was pioneered by A.B. Atkinson and F. Bourguignon (G.R. Feiwel (Ed.), Arrow and the Foundation of the Theory of Economic Policy, Macmillan, New York, 1987), who derive a sequential Lorenz dominance criterion for com-paring distributions with an identical population structure. In order to make their approach applicable to international comparisons, we extend their criterion to the case of different marginal distributions of household types, and derive a sequential stochastic dominance criterion that highlights the importance of first order dominance of the marginal distribution of household characteristics for obtaining consistent rankings of income distributions. Comparisons of distributions are made using the Luxembourg Income Study database for a number of countries.