  With one \Delta m^2 of the appropriate order of magnitude to solve the
atmospheric neutrino problem, we study the resulting three-generation
vacuum-oscillation fit to the solar neutrino flux. An explanation of the
atmospheric neutrino composition in terms of pure \nu_\mu \to \nu_\tau
oscillations is easily compatible with the well-known two-flavour oscillation
solution for solar neutrinos. The allowed parameter region in the
\sin^2(2\theta_{12})--\Delta m^2 plane changes little with increasing values of
the mixing element U_{e3}, provided this is less than about 0.4. We find that
the threefold maximal mixing is disfavoured.
