Computations have been made using a new program for the sub-photospheric layers, including opacity effects due to the negative hydrogen ion and to Rayleigh scattering. Under thermodynamic conditions completely convective models are found to occur, but displaced towards later types in the H–R diagram than those obtained by Hayashi. The models investigated range from the late K subclasses to about M3. Non-thermodynamic effects are considered. It appears that free electrons produced by high-energy particles are capable of modifying the results by reducing the effective temperature and luminosity, but not by completely removing the convective structure. Nor does it seem likely that opacity effects due to solid particles can destroy the convective structure. The possibility remains, however, that convective efficiency in the sub-photospheric layers was much reduced by a magnetic field at the stage where the planetary material separated from the Sun, and during the condensation of the first planetesimals and of the parent bodies of the meteorites. Only by a suppression of the high-luminosity convective models during this phase does it seem possible to explain the presence of water in meteorites, and the likely presence of any icy matrix in the first planetesimals.