An active phase-controlling scheme based on a proportional-integral-derivative-controlled piezoelectric transducer is presented with the purpose of stabilizing a quasi-zero-background absorption spectrometer. A fiber-based balanced Michelson interferometer is used, and absorption due to a gas sample in one of its arms results in an increased light signal to a detector, which otherwise, thanks to destructive interference, experiences a very low light level. With the presented approach, the sensitivity of already potent absorption measurement techniques, e.g., based on modulation, could be improved even further.