  In this work we focus on the Carroll-Field-Jackiw (CFJ) modified
electrodynamics in combination with a CPT-even Lorentz-violating contribution.
We add a photon mass term to the Lagrange density and study the question
whether this contribution can render the theory unitary. The analysis is based
on the pole structure of the modified photon propagator as well as the validity
of the optical theorem. We find, indeed, that the massive CFJ-type modification
is unitary at tree-level. This result provides a further example for how a
photon mass can mitigate malign behaviors.
