  We study a two-dimensional fluid of particles interacting through a
spherically-symmetric and marginally soft two-body repulsion. This model can
exist in three different crystal phases, one of them with square symmetry and
the other two triangular. We show that, while the triangular solids first melt
into a hexatic fluid, the square solid is directly transformed on heating into
an isotropic fluid through a first-order transition, with no intermediate
tetratic phase. In the low-pressure triangular and square crystals melting is
reentrant provided the temperature is not too low, but without the necessity of
two competing nearest-neighbor distances over a range of pressures. A whole
spectrum of water-like fluid anomalies completes the picture for this model
potential.
