[en] Mikheyev and Smirnov have shown that the interactions of neutrinos with matter can result in the conversion of electron neutrinos produced in the center of the sun to muon neutrinos. Bethe has exploited this and has pointed out that the solar-neutrino puzzle can be resolved if the mass difference squared of the two neutrinos is m₂² - m ₁² approx. = 6 x 10^-5 eV², and the mixing angle satisfies sin theta/sub v/ > 0.0065. We discuss a qualitatively different solution to the solar-neutrino puzzle which requires 1.0 x 10^-8 < (m₂² - m₁²) (sin² 2theta/sub v//cos 2theta/sub v/) < 6.1 x 10^-8 eV². Our solutions result in a much smaller flux of neutrinos from the p - p process than predicted by standard solar models, while Bethe's solution results in a flux of neutrinos from the p - process that is about the same as standard solar models