  We examine one of the standard loci for studying electromagnetic wave
emission -- the radiation from an oscillating electric dipole -- in a model in
which the electromagnetic sector is modified to include novel CPT- and
Lorentz-violating propagation effects involving a preferred axial vector
background. We evaluate the vacuum-birefringent radiation fields, including
nonperturbative terms where appropriate. In general, the energy-momentum
carried by the fields in this model is known to have a complicated
nonperturbative structure, which cannot be captured by naive power series
expansions in the components of the preferred background vector. However, we
nevertheless find that at the lowest nontrivial orders, there are actually no
modifications to the Larmor expressions for the energy-momentum emission.
