We present detailed measurements of the linewidth enhancement factor (LEF) of a quantum-dot distributed-feedback laser emitting around 1.3 mum above and below threshold. The above threshold method is based on the measurement of the frequency modulation and amplitude modulation response of the laser and shows significant dependence on modulation frequency. Drive current dependent measurements with both methods yield LEF values between 1 well below and 3 well above threshold, converging around 2 close to threshold.