  In the study of Planck-scale ("quantum-gravity induced") violations of
Lorentz symmetry, an important role was played by the deformed-electrodynamics
model introduced by Myers and Pospelov. Its reliance on conventional effective
quantum field theory, and its description of symmetry-violation effects simply
in terms of a four-vector with nonzero component only in the time-direction,
rendered it an ideal target for experimentalists and a natural concept-testing
ground for many theorists. At this point however the experimental limits on the
single Myers-Pospelov parameter, after improving steadily over these past few
years, are "super-Planckian", {\it i.e.} they take the model out of actual
interest from a conventional quantum-gravity perspective. In light of this we
here argue that it may be appropriate to move on to the next level of
complexity, still with vectorial symmetry violation but adopting a generic
four-vector. We also offer a preliminary characterization of the phenomenology
of this more general framework, sufficient to expose a rather significant
increase in complexity with respect to the original Myers-Pospelov setup. Most
of these novel features are linked to the presence of spatial anisotropy, which
is particularly pronounced when the symmetry-breaking vector is space-like, and
they are such that they reduce the bound-setting power of certain types of
observations in astrophysics.
