  We show that radiofrequency (RF) radiation may be used to create Feshbach
resonances in ultracold gases of alkali-metal atoms at desired magnetic fields
that are convenient for atomic cooling and degeneracy. For the case of
$^{39}$K+$^{133}$Cs, where there are no RF-free resonances in regions where Cs
may be cooled to degeneracy, we show that a resonance may be created near 21~G
with 69.2~MHz RF radiation. This resonance is almost lossless with circularly
polarized RF, and the molecules created are long-lived even with
plane-polarized RF.
