  We systematically examine how long-range hopping and its synergy with
extended interactions leads to light bound pairs. Pair properties are
determined for a dilute extended Hubbard model with large on-site repulsion
($U$) and both near- and next-nearest neighbour hopping ($t$ and $t'$) and
attraction ($V$ and $V'$), for cubic and tetragonal lattices. The presence of
$t'$ and $V'$ promotes light pairs. For tetragonal lattices, $t'<0$ pairs can
be lighter than non-interacting particles, and $d$-symmetric pairs form. Close
packing transition temperatures, $T^{\ast}$ are estimated for the Bose-Einstein
condensation (BEC) of pairs to be $k_{B}T^{\ast}\sim\overline{t} 0.1$, where
$\overline{t}$ is the geometric mean of the hoppings on the Cartesian axes.
When pairs have $d$-symmetry, the condensate has $d$-wave character. Thus, the
presence of both $t'$ and $V'$ leads ubiquitously to small strongly bound pairs
with an inverse mass that is linear in hopping, which could lead to high
temperature BECs.
