  We determine the neutrino mixing and mass parameters that are allowed by the
Super-Kamiokande atmospheric neutrino data in a three-neutrino model with one
mass-squared difference contributing to the oscillations. We find that although
$\nu_\mu\to\nu_\tau$ oscillations are favored, $\nu_\mu\to \nu_e$ oscillations
with amplitude as large as 0.18 are allowed even after accounting for the limit
from the CHOOZ reactor experiment. The range of allowed parameters permit
observable $\nu_\mu\leftrightarrow\nu_e$ and $\nu_e\to\nu_\tau$ oscillations in
future long-baseline experiments.
