Abstract: A system for balancing rotating members comprising a laser head which emits a laser shot in response to a laser control signal to remove material from the rotating member. The laser control signal is produced by a computer which is responsive to a plurality of signals representing vibration of the rotating member and influence coefficients from a memory device. The computer applies less than a calculated number of laser shots at each targeted location of the rotating member and then applies this reduced number sequentially to all targeted locations while calculating whether the vibration signals fall below targeted levels and, if so, discontinuing removal of material by the laser.