[en] The effect of modulation p-doping on multi-state lasing in InAs/InGaAs quantum dot (QD) lasers is studied for different levels of acceptor concentration. It is shown that in case of the short laser cavities, p-doping results in higher output power of the ground-state optical transitions of InAs/InGaAs QDs whereas in longer samples p-doping may result in the decrease of this power component. On the basis of this observation, the optimal design of laser active region and optimal doping level are discussed in details. (paper)