Using photoelectron spectroscopy, we have observed alkali anion photodesorption from alkali-halide cluster anions that contain two weakly bound electrons. In the alkali iodides, we have found this type of desorption in almost every (MI)(n)M- cluster we have studied (M=Na, K, Cs; n<9), although it depends on the probe laser frequency and cluster temperature. Using pump-probe techniques, we have shown that the process occurs on a picosecond time scale by way of an electronic excitation of the cluster's spin-paired electrons.