We propose a method to reach conditions of high degeneracy in a trapped Fer
mi gas, based on the adiabatic transfer of a small fraction of atoms from a
magnetic to a tighter optical trap. The transformation yields a large incr
ease of the Fermi energy, without a significant change of the temperature.
The large enhancement of the central, density emphasizes the role of the in
teractions and makes the system much closer to the BCS transition. We show
that, despite Pauli blocking, the thermalization processes ensuring equilib
rium in the optical trap are not suppressed at low temperature.