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We examine the efficiency with which light is reflected back into a single-mode fiber by front surface and multilayer dielectric mirrors. Coupling losses are due to the penetration of light into a multi-layer dielectric mirror, fiber-mirror separation, mirror tilt, and polishing-induced curvature of the fiber-end face. We also discuss the degradation of the coupling efficiency due to random errors of the optical layer thickness of dielectric mirrors. The results of this paper are needed for the discussion of the performance of a fiber Fabry-Perot interferometer to he presented in a companion paper.