  We enlarge the lepton sector of the Standard Model by adding to it two
right-handed neutrino singlets, and propose a model based on the seesaw
mechanism and on the lepton number $\bar L = L_e - L_\mu - L_\tau$. The model
is innovative from the theoretical point of view in that the $\bar L$-invariant
mass term of the right-handed neutrinos is associated with the large mass scale
responsible for the seesaw mechanism, whereas $\bar L$ is softly broken at a
smaller scale by the remaining Majorana mass terms of the right-handed
neutrinos. While being very economical, the model has predictive power: one
neutrino is massless ($m_3 = 0$), the lepton mixing matrix $U$ features $U_{e3}
= 0$, and the solar-neutrino oscillations have maximal amplitude.
