We show how a 17 keV neutrino, the solar neutrino problem, and the
atmospheric muon-neutrino deficit could all be the low-energy residues of the
same pattern of lepton-number breaking at and above the weak scale, with no
requirement for fine-tuning a symmetry-breaking scale at lower energies. Talk
given at ``Beyond the Standard Model III'', Carleton University, June 1992.