We consider the possibility of implementation of a free-electron maser with a two-mirror resonator composed of modified and conventional Bragg mirrors, operated in the short-wave part of the millimeter-wave range. The use of a modified Bragg mirror based on the traveling and quasicritical wave coupling at the input of the interaction space permits the transverse-index selection of modes. Amplification of the synchronous co-propagating wave by an electron beam is reached mainly in the regular part of the resonator. Even slight reflections from the conventional output Bragg cavity, which directly couples the co-and counter-propagating traveling waves, turn out to be sufficient for generation of self-excited oscillations. It is shown that the new scheme of a freeelectron maser ensures the oscillation frequency stabilization with respect to the electron-energy variation. With the optimal choice of the parameters, the oscillation frequency is close to the cutoff frequency of a quasi-critical wave excited in the modified Bragg structure.1) The Bragg resonators with two counter-propagating waves coupled by weakly corrugated waveguides, which were proposed in [1-3], are widely used at present in high-power microwave oscillators with curvilinear relativistic electron beams [4][5][6][7][8]. These moderately overdimensional resonators ensure feedback in a relatively narrow frequency range and, simultaneously, form a channel for transport of intense electron beams. Among the sources of this rating, the record-breaking parameters have been obtained in a freeelectron maser (FEM), which was implemented on the basis of an LIU-3000 accelerator in a combined experiment of the Joint Institute for Nuclear Research (JINR, Dubna) and the Institute of Applied Physics of the Russian Academy of Sciences (IAP RAS, Nizhny Novgorod) [8]. Pulses with a peak power of 20 MW, a duration of 200 ns, a pulse repetition rate of up to 1 Hz, and a spectrum width of about 6 MHz, which is close to the theoretical limit, were obtained at a frequency of 30 GHz.One of the main directions of these studies is forwarding of FEMs into the shorter-wave ranges, which requires that the overdimensionality of the operation space is increased with the preservation of the selective properties of the electrodynamical system. Research experience shows that in the traditional variant of a Bragg resonator, the problems with the excitation of different pairs of cylindrical-wavequide modes, which are related to Bragg corrugation and, correspondingly, have different oscillation frequencies, arise even if the resonator has a diameter D ∼ 2λ, where λ is the radiation wavelength. Thus, it becomes a topical problem to increase the selective capabilities of the Bragg resonators. This can be done by using the modified Bragg