  Focusing on gauge degrees of freedom specified by a 1+3 dimensions model
hosting a Maxwell term plus a Lorentz and CPT non-invariant Chern-Simons-like
contribution, we obtain a minimal extension of such a system to a
supersymmetric environment. We comment on resulting peculiar self-couplings for
the gauge sector, as well as on background contribution for gaugino masses.
Furthermore, a non-polynomial generalization is presented.
