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A low probability of intercept (LPI) waveform is designed to appear to the target it probes as noise, and consequently the robust target receiver can detect only a rise in random energy. It can be recalled by the transmitter (platform), and matched to what is received; however, the platform pays a heavy two-way attenuation penalty: its signal-to-noise ratio (SNR) is far lower than that at the target. How these two factors trade off against one another is the topic of this paper. It will be shown that the sonar's time-bandwidth product is generally unfavorable to LPI. For most cases of interest in a Gaussian noise environment, LPI sonar does not favor covert observation for sonar signals shorter than 1 min at ranges greater than 100 yards. However, LPI sonar may have a key role in non-Gaussian heavy-tailed noise environments. Specifically, LPI may play a role in environments where the ambient noise has a kurtosis of around 10.