Finite mixtures of log-normal prove to be very useful when analyzing inequality and inequality decomposition.Firstof 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 analyse 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.