  We study neutrino oscillations and the level-crossing probability PLZ in
power-law potential profiles A(r)\propto r^n. We give local and global
adiabaticity conditions valid for all mixing angles theta and discuss different
representations for PLZ. For the 1/r^3 profile typical of supernova envelopes
we compare our analytical to numerical results and to earlier approximations
used in the literature. We then perform a combined likelihood analysis of the
observed SN1987A neutrino signal and of the latest solar neutrino data,
including the recent SNO CC measurement. We find that, unless all relevant
supernova parameters (released binding energy, \bar\nu_e and \bar\nu_{\mu,\tau}
temperatures) are near their lowest values found in simulations, the status of
large mixing type solutions deteriorates considerably compared to fits using
only solar data. This is sufficient to rule out the vacuum-type solutions for
most reasonable choices of astrophysics parameters. The LOW solution may still
be acceptable, but becomes worse than the SMA-MSW solution which may, in some
cases, be the best combined solution. On the other hand the LMA-MSW solution
can easily survive as the best overall solution, although its size is generally
reduced when compared to fits to the solar data only.
