In this work, transition processes and a stationary regime of a single-atom laser with incoherent pumping under conditions of the strong-coupling and bad-cavity limit have been studied. In the thresholdless regime, our numerical results were compared with corresponding experimental data. The amplitude and the frequency of the relaxation oscillations as the functions of the incoherent pumping value were also analyzed. The pumping strength was established to have a very significant effect on the amplitude of these oscillations and no appreciable effect on their frequency. The possibility of the noise reduction by means of increasing of the number of atoms in the cavity was discussed.