Just-So Oscillation: as Just as MSW?

The neutrino long wavelength (just-so) oscillation is reconsidered as a solution to the solar neutrino problem. In the light of the presently updated results of the four solar neutrino experiments, the data fit in the just-so scenario substantially improves and becomes almost as good as in the MSW scenario. Surprising result of our analysis is that best fit is achieved when the oscillation occurs only between two neutrino states: switching on the oscillation into third neutrino increases the $\chi^2$ value. Namely, we consider the vacuum oscillation scenario in the three-neutrino system (4 parameters) and find out that the $\chi^2$ minimum is always achieved in the {\it two} parameter subspace in which actually only {\it two} neutrino states oscillate. This holds in the framework of any solar model with relaxed prediction of the various neutrino fluxes. The possible theoretical implications of this observation are also discussed.