  The Yang-Mills (YM) equation in three spacetime dimensions (3D) can be
modified to include a novel parity-preserving interaction term, with inverse
mass parameter, in addition to a possible topological mass term. The novelty is
that the modified YM equation is not the Euler-Lagrange equation of any
gauge-invariant local action for the YM gauge potential alone. Instead,
consistency is achieved in the "third way" exploited by 3D "minimal massive
gravity". We relate our results to the "novel Higgs mechanism" for Chern-Simons
gauge theories.
