  The PMNS neutrino mixing matrix U_{PMNS} is in general a product of two
unitary matrices U_{lep} and U_{\nu} arising from the diagonalization of the
charged lepton and neutrino mass matrices, U_{PMNS} = U^{\dagger}_{lep}
U_{\nu}. Assuming that U_{\nu} is a bimaximal mixing matrix, we investigate the
possible forms of U_{lep}. We identify three possible generic structures of
U_{lep}, which are compatible with the existing data on neutrino mixing. One
corresponds to a hierarchical ``CKM-like'' matrix. In this case relatively
large values of the solar neutrino mixing angle \theta_{sol}, and of
|U_{e3}|^2, are typically predicted, \tan^2\theta_{sol} \gtap 0.42, |U_{e3}|^2
\gtap 0.02, while the atmospheric neutrino mixing angle \theta_{atm} can
deviate noticeably from \pi/4, \sin^2 2\theta_{atm} \gtap 0.95. The second
corresponds to one of the mixing angles in U_{lep} being equal to \pi/2, and
predicts practically maximal atmospheric neutrino mixing \sin^2 2\theta_{atm}
\simeq 1. Large atmospheric neutrino mixing, \sin^2 2\theta_{atm} \gtap 0.95,
is naturally predicted by the third possible generic structure of U_{lep},
which corresponds to all three mixing angles in U_{lep} being large. We focus
especially on the case of CP-nonconservation, analyzing it in detail. We show
how the CP-violating phases, arising from the diagonalization of the neutrino
and charged lepton mass matrices, contribute to the measured neutrino mixing
observables.
