  We propose the use of a combined optical dipole trap to achieve Fermi
degeneracy by sympathetic cooling with a different bosonic species. Two
far-detuned pairs of laser beams focused on the atomic clouds are used to
confine the two atomic species with different trapping strengths. We show that
a deep Fermi degeneracy regime can be potentially achieved earlier than
Bose-Einstein condensation, as discussed in the favorable situation of a
^6Li--^{23}Na mixture. This opens up the possibility of experimentally
investigating a mixture of superfluid Fermi and normal Bose gases.
