In this letter, we investigate the effects of annealing and p-doping on the two-state competition of 1.3 μm InAs/GaAs quantum-dot (QD) lasers. By analyzing the modal gain competition from below-ground-state (GS) to above-excited-state (ES) thresholds, we found that: 1) the onset of ES lasing can be significantly delayed to a higher injection current with optimum annealing conditions; and 2) under the same annealing condition, p-doped QD lasers can sustain GS lasing to higher operating temperature as compared to the intrinsic ones. Consequently, we believe that this letter will be beneficial to researchers working on QD lasers for uncooled operation.