In this paper we propose a nested inequality decomposition by income sources and population subgroups derived by the Theil index. We firstly motivate our preference for its associated decomposition by income sources with respect to the axiom-based proposal of Shorrocks (1982) and the Gini-based decomposition of Lerman and Yitzhaki (1985). Then we enhance the set of desirable proprieties able to sustain that choice with the additional requirement of subgroup decomposability. The nested decomposition of the Theil index allows the overall level of inequality to be function of only three types of factors: source-group income and population shares; source-group inequality. Finally, using LIS micro data on incomes, we apply it to the case of geographical disaggregation of inequality in Italy between 1989 and 2000.