We determine the neutrino parameters for MSW and vacuum oscillations (active and sterile neutrinos) that are allowed by the separate, and collective, imposition of the constraints from total event rates in the chlorine, GALLEX, SAGE, and SuperKamiokande experiments (504 days), the SuperKamiokande electron energy spectrum, and the SuperKamiokande zenith-angle dependence. The small mixing angle MSW solution is acceptable at the 7% C.L. (8% for sterile nu's) and the vacuum solution is acceptable at the 6% C.L. . The best-fit global MSW solution for active neutrinos is: Delta m^2 = 5 x 10^-6 eV^2, sin^2 (2 theta) = 5.5 x 10^{-3} (and for sterile neutrinos: Delta m^2 = 4 x 10^-6 eV^2, sin^2 (2 theta) = 7 x 10^-3). For vacuum oscillations, the best-fit solution is: Delta m^2 = 6.5 x 10^-11 eV^2, sin^2 (2 theta) = 0.75 . An arbitrary combination of undistorted (no oscillations) pp, 7Be, 8B, and CNO neutrino fluxes is inconsistent with the combined data sets at the 3.5 sigma C.L., independent of astrophysical considerations. We use improved calculations of solar model fluxes, neutrino absorption cross sections and energy spectra, and a detailed evaluation of regeneration effects.
