  We develop, clarify and test various aspects of cluster methods dynamical
mean field methods using a soluble toy model as a benchmark. We find that the
Cellular Dynamical Mean Field Theory (C-DMFT) converges very rapidly and
compare its convergence properties with those of the Dynamical Cluster
Approximation (DCA). We propose and test improved estimators for the lattice
self energy within C-DMFT.
