  We implement the contractor-renormalization method to study the checkerboard
Hubbard model on various finite-size clusters as function of the
inter-plaquette hopping t' and the on-site repulsion U at low hole doping. We
find that the pair-binding energy and the spin gap exhibit a pronounced maximum
at intermediate values of t' and U, thus indicating that moderate inhomogeneity
of the type considered here substantially enhances the formation of hole pairs.
The rise of the pair-binding energy for t'<t'_max is kinetic-energy driven and
reflects the strong resonating valence bond correlations in the ground state
that facilitate the motion of bound pairs as compared to single holes.
Conversely, as t' is increased beyond t'_max antiferromagnetic magnons
proliferate and reduce the potential energy of unpaired holes and with it the
pairing strength. For the periodic clusters that we study the estimated phase
ordering temperature at t'=t'_max is a factor of 2-7 smaller than the pairing
temperature.
