  $\gamma_5$ is notoriously difficult to define in $D$ dimensions. The
traditional BMHV scheme employs a non-anticommuting $\gamma_5$. Its key
advantage is mathematical consistency and the existence of all-order proofs.
Its disadvantage is the spurious breaking of gauge invariance in chiral gauge
theories like the electroweak standard model. Our research programme aims to
determine the special finite counterterms which are necessary to restore gauge
invariance, to allow more straightforward applications of the BMHV scheme and
to cross-check alternative schemes. In these proceedings we present the key
concepts and methods, and we outline the calculational procedure and present
results for an abelian gauge theory at the 2-loop level. An important
observation is the simplicity of the results -- three types of
symmetry-restoring counterterms are sufficient at the 2-loop level.

High Energy Physics - Phenomenology