  In this paper we investigate the thermodynamical properties of ``unbalanced''
superconductors, namely, systems where the electron-boson coupling $\lambda$ is
different in the self-energy and in the Cooper channels. This situation is
encountered in a variety of situation, as for instance in d-wave
superconductors. Quite interesting is the case where the pairing in the
self-energy is smaller than the one in the gap equation. In this case we
predict a finite critical value $\lambda_c$ where the superconducting critical
temperature $T_c$ diverges but the zero temperature gap is still finite. The
specific heat, magnetic critical field and the penetration depth are also
evaluated.
