The PMNS neutrino mixing matrix $U_{\rm PMNS}$ is in general a product
of two unitary matrices
$U_{\rm lep}$ and $U_{\nu}$
arising from the diagonalization of
the charged lepton and neutrino mass matrices,
$U_{\rm PMNS} = U^{\dagger}_{\rm lep} U_{\nu}$.
Assuming that $U_{\nu}$ is a bimaximal mixing matrix,
we investigate the possible forms of $U_{\rm lep}$.
We identify three possible
generic structures of $U_{\rm lep}$,
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 $\theta_{\rm sol}$,
and of $|U_{e3}|^2 \equiv |(U_{\rm PMNS})_{e3}|^2$,
are typically predicted,
$\tan^2\theta_{\rm sol} \gtap 0.42$,
$|U_{e3}|^2 \gtap 0.02$,
while the atmospheric
neutrino mixing angle $\theta_{\rm atm}$ can
deviate noticeably from $\pi/4$,
$\sin^22\theta_{\rm atm} \gtap 0.95$.
The second corresponds to
one of the mixing angles in $U_{\rm lep}$
being equal to $\pi/2$,
and predicts practically maximal atmospheric
neutrino mixing
$\sin^2 2 \theta_{\rm atm} \simeq 1$.
Large atmospheric neutrino
mixing, $\sin^22\theta_{\rm atm} \gtap 0.95$,
is naturally predicted by the third possible
generic structure of $U_{\rm lep}$,
which corresponds to all three
mixing angles in $U_{\rm lep}$ 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.
