  We present a search for non-zero theta_{13} and deviations of sin^2
theta_{23} from 0.5 in the oscillations of atmospheric neutrino data from
Super-Kamiokande -I, -II, and -III. No distortions of the neutrino flux
consistent with non-zero theta_{13} are found and both neutrino mass hierarchy
hypotheses are in agreement with the data. The data are best fit at Delta m^2 =
2.1 x 10^-3 eV^2, sin^2 theta_{13} = 0.0, and sin^2 theta_{23} =0.5. In the
normal (inverted) hierarchy theta_{13} and Delta m^2 are constrained at the
one-dimensional 90% C.L. to sin^2 theta_{13} < 0.04 (0.09) and 1.9 (1.7) x
10^-3 < Delta m^2 < 2.6 (2.7) x 10^-3 eV^2. The atmospheric mixing angle is
within 0.407 <= sin^2 theta_{23} <= 0.583 at 90% C.L.
