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The paper reports numerical calculations appropriate for the design of an "efficiency-enhanced" Raman free electron laser (FEL) oscillator. A helical undulator is used which consists of a constant period section followed by a section where the period is decreased roughly 10 percent. Simulation of the FEL is done by following the radiation dynamics in both the small- and large-signal regimes, using the "generalized pendulum equation" with self-consistent radiation field. It is found that the efficiency of the oscillator may be enhanced from Â¿ 8 (no taper) to Â¿ 15 percent (with taper). The configuration of an experimental oscillator is described; this device should produce Â¿ 25 MW at a wavelength Â¿ 1.8 mm using an 800-kV electron beam.