  Observations of atmospheric neutrinos are usually analyzed using the
simplifying approximation that either \(\nu_\mu \leftrightarrow \nu_\tau\) or
\(\nu_e \leftrightarrow \nu_\mu\) two-flavor mixing is relevant. Here we
instead consider the data using the simplifying approximation that only one
neutrino mass scale is relevant. This approximation is the minimal three-flavor
notation that includes the two relevant two-flavor approximations. The
constraints in the parameter space orthogonal to the usual, two-flavor analyses
are studied.
