The recent observations of atmospheric ν events from the Super-Kamiokande experiment are compatible with two-flavor oscillations in the νμ↔ ντ channel ("standard" interpretation). Among the possible deviations from this standard picture, we investigate two cases: (1) three-flavor oscillations and (2) a specific solution without oscillations (namely, neutrino decay). While the first solution appears perfectly viable, provided that the 3 ν oscillations occur dominantly in the νμ↔ ντ channel and subdominantly in the νμ↔ νe channel, the second is shown to be incompatible with the data. The derivation of such results is based on an updated analysis, including the latest 45 kTy data sample from Super-Kamiokande. A comparison with our previous results, based on 33 kTy data, shows that the oscillation evidence is strengthened, and that the neutrino mass-mixing parameters are constrained in smaller ranges.