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 $(\ensuremath{\Delta}{m}^{2},{\mathrm{tan}}^{2}\ensuremath{\theta})$ with $\ensuremath{\theta}\ensuremath{\in}(0,\ensuremath{\pi}/2).$ Recently, it was pointed out that the allowed region of parameters from a fit to the measured total rates can extend to values $\ensuremath{\theta}g~\ensuremath{\pi}/4$ (the so-called ``dark side'') when higher confidence levels are allowed. The purpose of this Rapid Communication is to reanalyze the problem, including all the solar neutrino data available, to discuss the dependence on the statistical criteria in the determination of the C.L. 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 are included, the regions extend more into the second octant.