The paper presents an analysis of the energetics of a few possible candidates for the structural model of the root 3 x root 30 degrees reconstruction of the alpha-SiC(0001) surface. The analysis is based on the semi-empirical, self-consistent, quantum mechanical cluster calculations of MNDO type (AMI parametrization). Models allowing clean stoichiometric, Si rich and C rich as well as hydrogenated surfaces were tested. The results indicate that, unlike in most cases with semiconductor surfaces, here, hydrogenation of the surface facilitates the reconstruction instead of lifting it. The most favourable model for the reconstruction from the calculated surface energy point of view is the one where hydrogenated triangles of C atoms saturate the surface silicon dangling bonds. The structure resembles that of cyclopropane with three of the C-H bonds substituted by the C-Si bonds.