Standard measures of multidimensional inequality (implicitly) assume common preferences for all individuals, and hence are not sensitive to preference heterogeneity among members of society. In this paper, we measure the inequality of the distribution of equivalent incomes, which is a preference-sensitive multidimensional wellbeing measure. To quantify the contribution of preference heterogeneity to wellbeing inequality, we use a decomposition method that calculates wellbeing inequality in different counterfactual distributions. We focus on four sources of wellbeing inequality: the correlation between outcomes and preferences, the preference heterogeneity, the correlation between the outcome dimensions, and the inequality within each of the outcome dimensions. We find that preference heterogeneity accounts for a considerable part of overall wellbeing inequality in Russia for the period 1995–2005.