  The $t-J$ and Heisenberg models are truncated expansions of a canonically
transformed Hubbard model coinciding with it at $U\to \infty$. We show that a
modified canonical transformation applied to the Hubbard model leads to
alternative models of the same form, but whose convergence properties with
respect to the expansion are more favourable, resulting in a good description
of the half-filled ground state even at $0<U\leq1$. We investigate the
transformed Hamiltonian and observables for metallic and insulating variational
wave-functions.
