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Present-day gyrotrons intended for plasma heating and current-drive experiments operate in high-order modes. Therefore, in such gyrotrons, in the process of voltage rise, as a rule, higher frequency parasitic modes are excited prior to the desired mode. This excitation can be avoided when electron beams with lower current density at intermediate voltages are used. Then, when the voltage passes through the region of excitation of high-frequency parasitic modes, the beam current can be made lower than the start current of those modes. At the same time, when the voltage reaches the excitation zone of the desired mode, the current can be high enough for exciting the desired mode. Such lowering of the beam current at intermediate voltages can be realized by reducing the ratio of the space-charge-limited to the temperature-limited emission. The method is illustrated by an example showing how the excitation of a TE23, 6-mode can be avoided in a gyrotron designed for operation at the TE22, 6-mode. Applicability of this method to millimeter-wave megawatt-class gyrotrons is discussed. The method proposed has additional advantages for gyrotrons operating in power-modulated regimes which are used for suppression of neoclassical tearing modes in large-scale tokamaks and stellarators.