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We report the development of a simple method for eliminating coherent background noise and fluctuations from saturation spectroscopy signals. With this technique, which utilizes a traveling-wave acousto-optic modulator to simultaneously frequency-shift and modulate the saturating beam, we have routinely observed zero background, Doppler-free saturation resonances in the $I2$ at 514.5 nm. With a low-noise laser or high pump modulation frequency, we have achieved detection sensitivity approaching the fundamental quantum limit.