I suggest a model based on a softly broken symmetry L-e-L-mu-L-tau and on B
abu's mechanism for the two-loop radiative generation of neutrino masses. T
he model predicts that one of the physical neutrinos (nu (3)) is massless a
nd that its component along the nu (e) direction (U-e3) is zero. Moreover,
if the soft-breaking term is assumed to be very small, then the vacuum osci
llations of nu (e) have almost maximal amplitude and solve the solar-neutri
no problem. New scalars are predicted in the 10 TeV energy range, and a bre
akdown of e-mu-tau universality should not be far from existing experimenta
l bounds..