It is shown that the flow-sensitive alternating inversion recovery (FAIR) technique is complicated by the effect of radiation damping, leading to problems in calibrating this method on phantoms and to inaccuracies in measured flows. A modified scheme called FAIRER (FAIR excluding radiation damping) is proposed, which suppresses the damping effects by employing very weak magnetic field gradients (0.06 G/cm) during the inversion recovery, spin-echo, and predelay periods. Results on phantoms and in vivo on cat brain are presented that demonstrate that FAIRER effectively solves these problems.