We investigate the saturation properties of four-wave mixing of short optical pulses in a semiconductor optical amplifier. By varying the gain of the optical amplifier, we find a strong dependence of both conversion efficiency and signal-to-background ratio on pulse width and bit rate. In particular, the signal-to-background ratio can be optimized for a specific amplifier gain. This behavior, which is coherently described in experiment and theory, is attributed to the dynamics of the amplified spontaneous emission, which is the main source of noise in a semiconductor optical amplifier.