  We present an analysis of the MSW neutrino oscillation solutions of the solar
neutrino problem in the framework of two-neutrino mixing in the enlarged
parameter space $(\Delta m^2, \tan^2\theta)$ with $\theta \in
(0,\frac{\pi}{2})$. Recently, it was pointed out that the allowed region of
parameters from a fit to the measured total rates can extend to values $\theta
\geq \frac{\pi}{4}$ (the so called ``dark side'') when higher confidence levels
are allowed. The purpose of this letter is to reanalize the problem including
all the solar neutrino data available, to discuss the dependence on the
statistical criteria in the determination of the CL of the ``dark side'' and to
extract the corresponding limits on the largest mixing allowed by the data. Our
results show that when the Super-Kamiokande data on the zenith angle
distribution of events and the spectrum information is included, the regions
extend more into the dark side.
