Acoustic feedback is capable of driving an electroacoustic amplification system unstable. Inserting a frequency shifter into the feedback loop can increase the maximum stable gain before instability. In this paper, we explain how frequency shifting can effectively smooth out the feedback loop magnitude response and how this relates to the system stability. Then we describe measurements on real acoustic systems that we employ to study the practical performance. Although useful for stabilizing systems in reverberant environments, reasonably small amounts of frequency shifting do not provide a significant benefit for hearing aids. It can be helpful to employ a microphone with a focused directivity pattern, and we describe how the directivity pattern may affect the efficacy of frequency shifting.