  We study Ising ferrimagnets on square lattices with antiferromagnetic
exchange couplings between spins of values S=1/2 and S=1 on neighbouring sites,
couplings between S=1 spins at next--nearest neighbour sites of the lattice,
and a single--site anisotropy term for the S=1 spins. Using mainly ground state
considerations and extensive Monte Carlo simulations, we investigate various
aspects of the phase diagram, including compensation points, critical
properties, and temperature dependent anomalies. In contrast to previous
belief, the next--nearest neighbour couplings, when being of antiferromagnetic
type, may lead to compensation points.
