The optical speed-up at transparency principle has been successfully applied to a gain-clamped semiconductor optical amplifier yielding a remarkable acceleration in the gain recovery of the device as well as to the disappearance of the typical relaxation oscillations stemming from the coupling between the internal lasing mode and the carrier density. A record gain recovery time of 13 ps has been measured with an available gain of still 16 dB. A small-signal analysis of the semiconductor laser amplifier rate equations properly reproduces the acceleration of the recovery time and the disappearance of the relaxation oscillations. These results apply to semiconductor lasers in general.