  We show that low-energy inelastic cross sections can decrease as well as
increase in the vicinity of a zero-energy Feshbach resonance. When an external
field is used to tune across such a resonance, the real and imaginary parts of
the scattering length show asymmetric oscillations, with both peaks and
troughs. In favorable circumstances the inelastic collision rate can be reduced
almost to zero. This may be important for efforts to achieve evaporative and
sympathetic cooling for molecules.
