Some while ago (Prentice 1973a) I demonstrated that if the present Sun were to possess a small burnt out central core of mass 2-3% M⊙ its neutrino flux would be a factor 10 or so smaller than that of conventional homogeneously evolved solar models. It was not, however, conclusively shown what conditions might lead to the formation of such a core or indeed whether a burnt out core could be attained after 4.7 × 109 yr. of nuclear evolution. In this connection Demarque et al. (1973) has considered the evolution of an initially inhomogeneous model consisting of a hydrogen free core surrounded by a homogeneous envelope.