  Gauge-fixed correlation functions are a valuable tool in intermediate steps
when determining gauge-invariant physics. However, when obtaining them in
different calculations, it is necessary to use exactly the same definition of
the gauge to ensure comparability. Beyond perturbation theory, this is
complicated by the Gribov-Singer ambiguity. In principle, lattice gauge theory
can manipulate individual Gribov copies, thus making it an excellent method to
deal with the ambiguity. However, to compare to continuum methods this requires
to replicate the same treatment outside the lattice, usually in a path integral
formulation. Here, the properties of the gauge orbit will be investigated with
respect to this question. Especially, the possibility of employing averages
over Gribov copies in non-perturbative generalizations of the Landau gauge will
be discussed.
