We consider a discretized Maier-Saupe model for a polydisperse solution of micelles of axial symmetry. An exact mean-held solution is presented. The phase diagram displays a biaxial phase at small average anisometries and finite dispersion in size, and two opposite uniaxial nematic phases for large average anisometries. Relations to the experimental phase diagram for ternary mixtures are discussed. (C) 1997 American Institute of Physics.