The seesaw mechanism of neutrino mass generation is analysed under the foll
owing assumptions: (1) minimal seesaw with no Higgs triplets, (2) hierarchi
cal Dirac masses of neutrinos, (3) large lepton mixing primarily or solely
due to the mixing in the right-handed neutrino sector, and (4) unrelated Di
rac and Majorana sectors of neutrino masses. It is shown that large mixing
governing the dominant channel of the atmospheric neutrino oscillations can
be naturally obtained and that this constrained seesaw mechanism favours t
he normal mass hierarchy for the light neutrinos leading to a small U-e3 en
try of the lepton mixing matrix and a mass scale of the lightest right hand
ed neutrino M similar or equal to 10(10) - 10(11) GeV. Any of the three mai
n neutrino oscillation solutions to the solar neutrino problem can be accom
modated. The inverted mass hierarchy and quasi-degeneracy of neutrinos are
disfavoured in our scheme. This talk is based on the work [1].