Static and dynamic characteristics of a quantum dot (QD) laser with double asymmetric barrier layers – an advanced type of semiconductor laser – are studied. Both direct and indirect capture of carriers into the lasing ground state in QDs is considered. The intradot relaxation of carriers, which controls the laser characteristics in the case of only indirect capture, is shown to not be a significant factor in the case of both direct and indirect capture. In the latter case, both the output optical power and modulation bandwidth are considerably increased.