  We propose an experimental procedure to cool fermionic atoms loaded into an
optical lattice. The central idea is to spatially divide the system into
entropy-rich and -poor regions by shaping the confining potential profile.
Atoms in regions of high entropy per particle are subsequently isolated from
the system. We discuss how to experimentally carry out this proposal, and
perform a quantitative study of its efficiency. We find that the entropy per
particle, $s$, can typically be reduced by a factor of 10 such that entropies
lower than $s/k_B \sim 0.2$ can be reached. Cooling into highly sought-after
quantum phases (such as an antiferromagnet) can thus be achieved. We show that
this procedure is robust against variations of the experimental conditions.
