  In the past, the possibility to employ (scalar) material reference systems in
order to describe classical and quantum gravity directly in terms of gauge
invariant (Dirac) observables has been emphasised frequently. This idea has
been picked up more recently in Loop Quantum Gravity (LQG) with the aim to
perform a reduced phase space quantisation of the theory thus possibly avoiding
problems with the (Dirac) operator constraint quantisation method for
constrained system. In this work, we review the models that have been studied
on the classical and/or the quantum level and parametrise the space of theories
so far considered. We then describe the quantum theory of a model that, to the
best of our knowledge, so far has only been considered classically. This model
could arguably called the optimal one in this class of models considered as it
displays the simplest possible true Hamiltonian while at the same time reducing
all constraints of General Relativity.
