In this paper, we propose an adaptive algorithm that iteratively updates both the weights and component parameters of a mixture importance sampling density so as to optimise the importance sampling performances, as measured by an entropy criterion. The method is shown to be applicable to a wide class of importance sampling densities, which includes in particular mixtures of multivariate Student distributions. The performances of the proposed scheme are studied on both artificial and real examples, highlighting in particular the benefit of a novel Rao-Blackwellisation device which can be easily incorporated in the updating scheme.