A FEL-oscillator with the traditional Bragg resonator consisting of the waveguide with corrugated ends (mirrors) allows to obtain single-mode generation with high efficiency. However, the output radiation frequency cannot be fixed more precisely than the mirror's reflection band, typically at 2–3%. There exists another scheme of the Bragg resonator without the smooth tube between mirrors. Depending on the corrugation phase shift between the mirrors this resonator has a single high-quality mode inside the reflection band or two modes near the ends of the reflection band. Variation of the corrugation phase shift from 0 to 2π tunes the mode frequency from higher to lower limit of the reflection band. Bragg resonators of this type were designed both for high-efficiency FEL-oscillator and for precise radiation frequency meter. Experimental investigation of the tunable FEL-oscillator is now in progress.