Weakness of the electron-wave coupling in compact low-power terahertz-frequency-range gyrotrons due to relatively low electron beam currents and operation at high cyclotron harmonics results in the use of long-length cavities with high diffraction Q-factors, and, therefore, with a high share of the ohmic loss of the radiated wave power. In this work, we demonstrate a possibility for stable operation at higher axial modes possessing relatively low diffraction Q-factors. Enhanced efficiency of the electron-wave interaction is provided due to the excitation of higher axial modes in the traveling-wave-tube regime.