  The most general, renormalizable Lagrangian that includes massive neutrinos
contains ``right-handed neutrino'' Majorana masses of order M. While there are
prejudices in favor of M much larger than the weak scale, virtually nothing is
known about the magnitude of M. I argue that the LSND anomaly provides,
currently, the only experimental hint: M around 1 eV. If this is the case, the
LSND mixing angles are functions of the active neutrino masses and mixing and,
remarkably, adequate fits to all data can be naturally obtained. I also discuss
consequences of this ``eV-seesaw'' for supernova neutrino oscillations, tritium
beta-decay, neutrinoless double-beta decay, and cosmology.
