Quantum-dot (QD) lasers exhibit many useful properties such as low threshold current, temperature and feedback insensitivity, chirpless behavior, and low linewidth enhancement factor (alphaH-factor). Although many breakthroughs have been demonstrated, the maximum modulation bandwidth remains limited in QD devices, and a strong damping of the modulation response is usually observed pointing out the role of gain compression. This paper investigates the influence of the gain compression in a 1.3-mum InAs-GaAs QD laser and its consequences on the above-threshold alphaH-factor. A model is used to explain the dependence of the alphaH-factor with the injected current and is compared with AM/FM experiments. Finally, it is shown that the higher the maximum gain, the lower the effects of gain compression and the lower the alphaH-factor. This analysis can be useful for designing chirpless QD lasers with improved modulation bandwidth as well as for isolator-free transmission under direct modulation.