  Zee-type models with Majorons naturally incorporate the 17 keV neutrino but
in their minimal version fail to simultaneously solve the solar neutrino
puzzle. If there is a sterile neutrino state, we find a particularly simple
solution to the solar neutrino problem, which besides $\nu_{17}$ predicts a
light Zeldovich-Konopinski-Mahmoud neutrino $\nu_{light}=\nu_e+\nu_{\mu}^c$
with a magnetic moment being easily as large as $10^{-11}\mu_B$ through the
Barr-Freire-Zee mechanism.
