Double-pass amplification of picosecond pulses is demonstrated and compared with single-pass amplification. This was achieved using a two-section tapered semiconductor optical amplifier with a chirped quantum-dot active region and a mode-locked laser diode as a seed. Across the range of biasing conditions common to both configurations, an enhancement in signal gain of up to 7 dB and output power by a factor of 4.1 was seen in the double-pass amplifier, compared to the single-pass. Only marginal increases in pulse duration were observed in the double-pass regime compared to the single-pass amplifier, meaning that enhancements in output power were well translated into peak power. Furthermore, the two-section contact layout of the SOA allowed the pulse duration to be optimised for a given fixed output power, giving additional flexibility to the amplifier. These results demonstrate the suitability of this simple and versatile technique, which could become the new standard in amplification of ultrashort pulses.