  The squeezing properties of a cavity Second Harmonic Generation (SHG) system
with an added Kerr effect-like nonlinearity are studied as a function of the
intra-cavity photon number. The competition between the second and the third
order non-linearities shifts the Hopf bifurcation of the standard SHG towards
higher intra-cavity energies eventually completely stabilizing the system.
Remarkably, the noise suppression is at the same time strongly enhanced, so
that almost perfect squeezing is obtained for arbitrarily large intra-cavity
photon numbers. Possible experimental implementations are finally discussed.
