SUMMARY The k principal points of a p-variate random vector X are defined as those points E, . k which minimize the expected squared distance between X and the nearest of the tj. This paper reviews some of the theory of principal points and redefines them in terms of self-consistent points. An anthropometrical problem which initiated the theoretical developments is described. Four methods of estimation, ranging from normal theory maximum likelihood to the usual k-means algorithm in cluster analysis, are introduced and applied to the example. Finally, a leave-one-out method is used to assess the performance of the four methods.