  Recent SNO results strongly favour the large mixing angle (LMA) MSW solar
solution. We argue that there are only two technically natural low energy
neutrino mass matrix structures consistent with the LMA MSW solution,
corresponding to either a hierarchy or an inverted hierarchy with pseudo-Dirac
neutrinos. We first present a model-independent analysis in which we
diagonalise each of these two mass matrix structures to leading order in
$\theta_{13}$ and extract the neutrino masses, mixing angles and phases. In
this analysis we express the MNS matrix to leading order in the small angle
$\theta_{13}$ including the neutrino {\em and} charged lepton mixing angles and
phases, the latter playing a crucial r\^{o}le for allowing the inverted
hierarchy case to be consistent with the LMA MSW solution. We then consider the
see-saw mechanism with right-handed neutrino dominance and show how the
successful neutrino mass matrix structures may be constructed with no tuning
and with small radiative corrections, leading to a full, partial or inverted
neutrino mass hierarchy. In each case we derive approximate analytic relations
between the input see-saw parameters and the resulting neutrino masses, mixing
angles and phases, which will provide a useful guide for unified model
building. For the hierarchical cases the LMA MSW solution gives a soft lower
bound $|U_{e3}|\simgt 0.1$, just below the current CHOOZ limit. Both
hierarchical and inverted hierarchical cases predict small $\beta \beta_{0\nu}$
with $|m_{ee}|\sim 0.01$ eV within the sensitivity of future proposals such as
GENIUS. Successful leptogenesis is possible if the dominant right-handed
neutrino is the heaviest one, but the leptogenesis phase is unrelated to the
MNS phases.
