  We explore the possibility that the 3 active (doublet) neutrinos have nearly
degenerate masses which are split only by the usual seesaw mechanism from 3
sterile (singlet) neutrinos in the presence of a softly broken $A_4$ symmetry.
We take the unconventional view that the sterile neutrinos may be light, i.e.
less than 1 keV, and discuss some very interesting and novel phenomenology,
including a connection between the LSND neutrino data and solar neutrino
oscillations.
