  Currently available estimates of the gluon-fusion effect in ultra-high energy
neutrino-nucleon interactions as well as in DIS on protons suffer from
uncertainty in defining the scattering profile function $\Gamma(b)$. Indeed,
the area, $S$, in the impact parameter space populated with interacting gluons
varies by a factor of $4 - 5$ from one analysis to another. To get rid of
uncertainties we specify the dipole-nucleon partial-wave amplitude $\Gamma(b)$
which meets the restrictions imposed by both the total dipole-nucleon cross
section and the small angle elastic scattering amplitude. The area $S$ becomes
a well defined quantity proportional to the diffraction cone slope. We solve
numerically the non-linear color dipole BFKL equation and evaluate the UHE
neutrino-nucleon total cross section. Our finding is that the saturation is a
rather weak effect, $\lsim 25%$, up to $E_{\nu}\sim 10^{12}$ GeV.
