Autonomous listening devices are increasingly used to study vocal aquatic animals, and there is a constant need to record longer or with greater bandwidth, requiring efficient use of memory and battery power. Real-time compression of sound has the potential to extend recording durations and bandwidths at the expense of increased processing operations and therefore power consumption. Whereas lossy methods such as MP3 introduce undesirable artifacts, lossless compression algorithms (e.g., flac) guarantee exact data recovery. But these algorithms are relatively complex due to the wide variety of signals they are designed to compress. A simpler lossless algorithm is shown here to provide compression factors of three or more for underwater sound recordings over a range of noise environments. The compressor was evaluated using samples from drifting and animal-borne sound recorders with sampling rates of 16-240 kHz. It achieves >87% of the compression of more-complex methods but requires about 1/10 of the processing operations resulting in less than 1 mW power consumption at a sampling rate of 192 kHz on a low-power microprocessor. The potential to triple recording duration with a minor increase in power consumption and no loss in sound quality may be especially valuable for battery-limited tags and robotic vehicles.