  We explore the properties of a new Maxwell electrodynamics coupled to a
Lorentz-violating background through the presence of higher-derivative terms.
Physical implications of this alternative effective theory modified by
Lorentz-violating operators of mass dimension-$5$ are considered, such as
modified dispersion relations which exhibit the vacuum birefringence
phenomenon. Subsequently, we analyze the energy-momentum tensor in the case we
reproduce the Gambini-Pullin electrodynamics. We explicitly show that for a
background time-like four-vector, $n^{\mu}$, the equations of motion indeed
reproduce those encountered by Gambini and Pullin in the framework of loop
quantum gravity . Finally, extended expressions for Maxwell-type equations are
written down in the case the external Lorentz-violating four-vector is
space-like.
