  We consider lepton mixing in an extension of the Standard Model with three
right-handed neutrino singlets. We require that the three lepton numbers L_e,
L_\mu, and L_\tau be separately conserved in the Yukawa couplings, and we
assume that they are softly broken only by the Majorana mass matrix M_R of the
neutrino singlets. In this framework, where lepton-number breaking occurs at a
scale much higher than the electroweak scale, deviations from
family-lepton-number conservation are calculable and finite, and lepton mixing
stems exclusively from M_R. We then show that a discrete symmetry exists such
that, in the lepton mixing matrix U, maximal atmospheric neutrino mixing
together with U_{e3}=0 can be obtained naturally. Alternatively, if one assumes
that there are two different scales in M_R and that the lepton number \bar L =
L_e - L_\mu - L_\tau is conserved in between them, then maximal solar neutrino
mixing follows naturally. If both the discrete symmetry and intermediate \bar L
conservation are introduced, bimaximal mixing is achieved.
