  A new general approach is introduced for definining an optimum zero-order
Hamiltonian for Rayleigh-Schr\"odinger perturbation theory. Instead of taking
the operator directly from a model problem, it is constructed to be a best fit
to the exact Hamiltonian within any desired functional form. When applied to
many-body perturbation theory for electrons, strongly improved convergence is
observed in cases where the conventional Fock hamiltonian leads to divergence
or slow convergence.
