  We consider the Lorentz-violating extended QED involving all nonminimal
dimension-5 additive CPT-odd terms. For this theory, we investigate the
possibility of generating the Carroll-Field-Jackiw (CFJ) term of the first
order in any of these nonminimal couplings. This term is demonstrated to vanish
in certain regularization schemes. We also study the question of
higher-derivative divergent contributions and demonstrate that they can be
eliminated by considering a given proportionality between the coefficients.
