Summary: We consider ways to estimate the mixing proportions in a finite mixture distribution or to estimate the number of components of the mixture distribution without making parametric assumptions about the component distributions. We require a vector of observations on each subject. This vector is mapped into a vector of 0s and 1s and summed. The resulting distribution of sums can be modelled as a mixture of binomials. We then work with the binomial mixture. The efficiency and robustness of this method are compared with the strategy of assuming multivariate normal mixtures when, typically, the true underlying mixture distribution is different. It is shown that in many cases the approach based on simple binomial mixtures is superior.