A typical problem of weakly relativistic low-power gyrotrons (especially in the case of operation at high cyclotron harmonics) is the use of long cavities ensuring extremely high diffraction Q-factors for the operating near-cutoff waves. As a result, a great share of the rf power radiated by electrons is spent in Ohmic losses. In this paper, we propose to use a sectioned cavity with π-shifts of the wave phase between sections. In such a cavity, a far-from-cutoff axial mode of the operating cavity having a decreased diffraction Q-factor is excited by the electron beam in a gyrotron-like regime.