We show theoretically that the use of a circular oversized waveguide with a helically corrugated internal surface as a dispersive medium ensures efficient compression of frequency-modulated microwave pulses up to peak powers of about 10 GW. According to the calculations, a pulse with the required frequency modulation can be obtained in a relativistic backward-wave oscillator operated in the 3-cm wavelength range and producing an output power of hundreds of megawatts. In a demonstration experiment, a 80-ns pulse of kilowatt power with frequency modulation in a 5% band was compressed to a 1.5-ns pulse with a 25-fold power amplification