  We analyse the renormalisation group flow of quantum gravity at sixth order
in the derivative expansion within the background field approximation.
Non-linear field redefinitions are used to ensure that only essential couplings
flow. Working within the universality class of General Relativity, with a
vanishing cosmological constant, redundant couplings are fixed to their values
at the Gaussian fixed point. This reduces the theory space to two dynamical
essential couplings given by Newton's and the Goroff-Sagnotti coupling.
Furthermore, it implements the condition that no extra degrees of freedom are
present beyond those of General Relativity, in contrast to higher derivative
theories and derivative expansions in a conventional renormalisation scheme. We
find a unique ultraviolet fixed point with a single relevant direction and
analyse the phase diagram of the theory. Our results suggest resilience of the
gravitational Reuter fixed point under the inclusion of higher order curvature
invariants and show several signs of near-perturbativity. The regulator
dependence of our results is investigated in detail and shows that qualitative
and quantitative features are robust to a large extent.
