A model with quasi-normal occupancy is applied to several typical high
-T-c superconductors obtaining tighter-bound Cooper fermion pairs. Wit
hin this model a small energy gap of the order of the Debye energy nea
r the Fermi surface is proposed. An important physical requirement of
the model is that the anomaly in the occupancy occurs simultaneously t
o the pair formation. The role of the variation of the ratio R = 2 Del
ta(0)/kT(c) in the range 2 - 10 is studied. The phonon barrier can be
overcomed and then obtain a good description of high-T-c superconducto
r cuprates in all the range of values for R suggested by experimental
results.