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Recent SNO results strongly favour the large mixing angle (LMA) MSW solarsolution. We argue that there are only two technically natural low energyneutrino mass matrix structures consistent with the LMA MSW solution,corresponding to either a hierarchy or an inverted hierarchy with pseudo-Diracneutrinos. We first present a model-independent analysis in which wediagonalise each of these two mass matrix structures to leading order in$\theta_{13}$ and extract the neutrino masses, mixing angles and phases. Inthis analysis we express the MNS matrix to leading order in the small angle$\theta_{13}$ including the neutrino {\em and} charged lepton mixing angles andphases, the latter playing a crucial r\^{o}le for allowing the invertedhierarchy case to be consistent with the LMA MSW solution. We then consider thesee-saw mechanism with right-handed neutrino dominance and show how thesuccessful neutrino mass matrix structures may be constructed with no tuningand with small radiative corrections, leading to a full, partial or invertedneutrino mass hierarchy. In each case we derive approximate analytic relationsbetween the input see-saw parameters and the resulting neutrino masses, mixingangles and phases, which will provide a useful guide for unified modelbuilding. For the hierarchical cases the LMA MSW solution gives a soft lowerbound $|U_{e3}|\simgt 0.1$, just below the current CHOOZ limit. Bothhierarchical and inverted hierarchical cases predict small $\beta \beta_{0\nu}$with $|m_{ee}|\sim 0.01$ eV within the sensitivity of future proposals such asGENIUS. Successful leptogenesis is possible if the dominant right-handedneutrino is the heaviest one, but the leptogenesis phase is unrelated to theMNS phases.Comment: Version published in JHEP09(2002)01

Constructing the large mixing angle MNS matrix in see-saw models with right-handed neutrino dominance