  We discuss cooling efficiency for different-species Fermi-Bose mixtures in
magnetic traps. A better heat capacity matching between the two atomic species
is achieved by a proper choice of the Bose cooler and the magnetically
trappable hyperfine states of the mixture. When a partial spatial overlap
between the two species is also taken into account, the deepest Fermi
degeneracy is obtained for an optimal value of the trapping frequency ratio.
This can be achieved by assisting the magnetic trap with a deconfining light
beam, as shown in the case of fermionic 6Li mixed with 23Na, 87Rb, and 133Cs,
with optimal conditions found for the not yet explored 6Li-87Rb mixture.
