  Inverse melting is the phenomenon, observed in both Helium isotopes, by which
a crystal melts when cooled at constant pressure. I investigate discrete-space
analogs of inverse melting by means of two instances of a
triangular-lattice-gas system endowed with a soft-core repulsion and a
short-ranged attraction. To reconstruct the phase diagram, I use both
transfer-matrix and Monte Carlo methods, as well as low-temperature series
expansions. In one case, a phase behavior reminiscent of Helium emerges, with a
loose-packed phase (which is solid-like for low temperatures and liquid-like
for high temperatures) extending down to zero temperature for low pressures and
the possibility of melting the close-packed solid by isobaric cooling. At
variance with previous model studies of inverse melting, the driving mechanism
of the present phenomenon is mainly geometrical, related to the larger
free-energy cost of a ``vacancy'' in the loose-packed solid than in the
close-packed one.
