  The incompatibility of explicit diffeomorphism violation with Riemannian
geometry within the gravitational Standard-Model Extension (SME) is revisited.
We review two methods of how to deal with this problem. The first is based on
an approach proposed originally by St\"{u}ckelberg and the latter is to
restrict spacetime geometry via the dynamical field equations and the second
Bianchi identity. Moreover, a third technique is introduced, which is novel and
relies on isometries of a gravitational system. Our conclusion is that an SME
background field configuration compatible with Riemannian geometry is more
likely to be determined the more diffeomorphisms are isometries of the
particular system. This finding has the potential to provide an alternative
treatment of explicit spacetime symmetry violation in gravity.
