Low probability of detection (LPD) communications are conducted at a low received signal-to-noise ratio (SNR) to deter eavesdroppers to sense the presence of the transmitted signal. Successful detection at intended receiver heavily relies on the processing gain achieved by employing the direct-sequence spread-spectrum (DSSS) technique. For scenarios that lack a sufficiently low SNR to maintain LPD, another metric, referred to as low probability of interception (LPI), is of interest to protect the privacy of the transmitted information. If covert communications take place in underwater acoustic (UWA) environments, then additional challenges are present. The time-varying nature of the UWA channel prevents the employment of a long spreading waveform. Furthermore, UWA environments are frequency-selective channels with long memory, which imposes challenges to the design of the spreading waveform. In this paper, a covert UWA communication system that adopts the DSSS technique and a coherent RAKE receiver is investigated. Emphasis is placed on the design of a spreading waveform that not only accounts for the transceiver structure and frequency-selective nature of the UWA channel, but also possesses a superior LPI. The proposed techniques are evaluated using both simulated and SPACE'08 in-water experimental data.