We further study a predictive model for the masses and mixing matrix of three Majorana neutrinos. At zeroth order the model yielded degenerate neutrinos and a generalized "tribimaximal" mixing matrix. At first order the mass splitting was incorporated and the tribimaximal mixing matrix emerged with very small corrections but with a zero value for the parameter s13. In the present paper a different, assumed weaker, perturbation is included which gives a non zero value for s13 and further corrections to other quantities. These corrections are worked out and their consequences discussed under the simplifying assumption that the conventional CP violation phase vanishes. It is shown that the existing measurements of the parameter s23 provide strong bounds on s13 in this model.