We investigate the minimum optical pulsewidth that is obtainable in the gain-switched distributed-feedback semiconductor laser. The minimum obtainable optical pulsewidth is determined by either the period doubling or the saturation of modulation efficiency, The shift of the resonance frequency to the lower frequency side with increase of the modulation current brings about these phenomena. It is predicted theoretically that the minimum obtainable pulsewidth is about 0.2 times the period of the small-signal resonance. The minimum pulsewidth after compression with a dispersion compensating fiber is also discussed. Experimental measurements are in good agreement with the theory.