Absolute cross sections for electron-impact detachment and electron-impact dissociation of CN- and BO- were measured for electron energies from threshold to 40 eV. With both ions we see only little dissociation when electron detachment occurs. In the case of CN- a resonance in the detachment cross section is discovered at an energy of similar to 10 eV. No resonances were seen in the case of BO-. We argue that the resonance observed for CN- is due to an excited state of the dianion. The nonresonant part of the detachment cross section is found to follow the classical prediction given by Andersen [Phys. Rev. Lett. 74, 892 (1995)].