Finite mixtures of log-normal prove to be very useful when analyzing inequality and inequality decomposition. First of all, under suitable prior information, we can try to identify each member of the mixture with a social group according to its income level. Second, using decomposable indices, we can analyze inequality inside each group and between the groups identified by the mixture. Finally, the possibility of Rao-Blackwellization can help to improve the precision of inference results for these indices, knowing that a finite mixture of log-normal provides conditional analytical results for conditional moments of these indices.