  The evidence for $\nu_\mu$ disappearance in the Super-Kamiokande atmospheric
neutrino experiment and the negative searches for $\nu_e$ disappearance in the
CHOOZ reactor experiment can be easily reconciled by assuming oscillations with
large amplitude in the $\nu_\mu\leftrightarrow\nu_\tau$ channel and small (or
null) amplitude in the $\nu_\mu\leftrightarrow\nu_e$ channel. It has been
claimed, however, that some oscillation scenarios with large
$\nu_\mu\leftrightarrow\nu_e$ mixing can also be constructed in agreement with
the present data. We investigate quantitatively two such scenarios: (a)
threefold maximal mixing; and (b) attempts to fit all sources of evidence for
oscillations (solar, atmospheric, and accelerator) with three neutrinos. By
using mainly Super-Kamiokande data, we show that the case (a) is disfavored,
and that the case (b) is definitely ruled out.
