It is shown for a precisely aligned electron beam of small thickness in a large-orbit gyrotron that high cyclotron harmonics (up to s⩽5) can be selectively excited with an electronic efficiency that is acceptable for some applications (1–10%). When the quality of the electron beam is high, the selective properties are maintained even for modes with high radial indices, raising hopes that this method can be used to obtain coherent radiation not only in the millimeter but also in the entire submillimeter wavelength range. A method for taking into account the space-charge effects is developed, and it is shown that the corresponding effects can be important at relatively small values of the electron pitch factor. The results of the analysis and preliminary experiments reveal the possibility of creating high-power compact sources of submillimeter radiation for the spectroscopy of various media, the diagnostics of dense plasmas, and some other applications.