High Tc superconductors all have their Fermi level in the middle of a high peak of the density of states (DOS). This explains the value of lambda, but is not enough to explain their high critical temperature : high DOS is usually associated with a narrow band width, which, as shown by Anderson, prevents the renormalization of mu into mu*, thus diminishing or suppressing Tc. Usually, a sufficient normalisation is still possible since the peak is set on a broader band. We calculated the Tc for compounds of the C-60 family : the basis of the peak is not very broad, but the neighbouring bands are very rich in electrons and help the renormalization. The results are in good agreement with experiments. The model also explains the variation of Tc with applied pressure and the discrepancy between the measured value of the coherence length and the expected value obtained from the Fermi velocity.