For unobtrusive capturing of acoustic breathing signals during sleep, a microphone can be placed in the vicinity of the person. As breathing signals are generally very weak compared to the intrinsic noise of the microphone, the resulting signal-to-noise ratio (SNR) is low. We present a de-noising technique for the enhancement of acoustic breathing signals captured with a microphone. As the intrinsic noise of the microphone is stationary, we can use standard spectral subtraction schemes with stationary noise-floor estimators. For bad SNR conditions however, these techniques suffer from musical tones. To remove these musical tones, we apply median filtering in the standard spectral subtraction scheme. Furthermore, an alternative solution is proposed that has a very low computational complexity.