  A method of cluster diagonalization in a systematically expanded Hilbert
space is described. We discuss some applications of this procedure to models of
high-T_c superconductors, like the t - J and one and three bands Hubbard models
in two dimensions. The results obtained with this method are compared against
results obtained with other techniques dealing with truncated Hilbert spaces.
The relation between this method of diagonalization in a reduced Hilbert space,
and perturbation theory and variational techniques is also discussed.
