  The gauge-invariant Chern-Simons-type Lorentz- and CPT-breaking term is here
re-assessed and issues like causality, unitarity, spontaneous gauge-symmetry
breaking are investigated. Moreover, 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.
