  We propose a new seesaw mechanism for neutrino masses within a class of
supersymmetric SO(10) models with broken D-parity. It is shown that in such
scenarios the B-L scale can be as low as TeV without generating inconsistencies
with gauge coupling unification nor with the required magnitude of the light
neutrino masses. This leads to a possibly light new neutral gauge boson as well
as relatively light quasi-Dirac heavy leptons. These particles could be at the
TeV scale and mediate lepton flavour and CP violating processes at appreciable
levels.
