  The systematics of different approximations within the self-energy-functional
theory (SFT) is discussed for fermionic lattice models with local interactions.
In the context of the SFT, an approximation is essentially given by specifying
a reference system with the same interaction but a modified non-interacting
part of the Hamiltonian which leads to a partial decoupling of degrees of
freedom. The reference system defines a space of trial self-energies on which
an optimization of the grand potential as a functional of the self-energy
Omega[Sigma] is performed. As a stationary point is not a minimum in general
and does not provide a bound for the exact grand potential, however, it is {\em
a priori} unclear how to judge on the relative quality of two different
approximations. By analyzing the Euler equation of the SFT variational
principle, it is shown that a stationary point of the functional on a subspace
given by a reference system composed of decoupled subsystems is also a
stationary point in case of the coupled reference system. On this basis a
strategy is suggested which generates a sequence of systematically improving
approximations. The discussion is actually relevant for any variational
approach that is not based on wave functions and the Rayleigh-Ritz principle.
