BPSK signals have been defined for transmission through a shallow-water acoustic communication channel. The signals were accompanied by two displaced carriers to facilitate carrier recovery. To correct for the adverse effects of time spreading, a pseudo-random learning sequence was transmitted ahead of the communication signal. The signal processing consists of a shift to baseband guided by the displaced carriers, a least-squares equalizer tuned to the received learning signal, coherent addition of reconstructed baseband signals (corresponding to selected channels of the receiving hydrophone array), and bit restoration with a decision-directed equalizer. In this manner, bit rates up to 4 kbit/s are successfully dealt with in moving-point-to-fixed-point communication. The main risk appears to be the fading of a displaced carrier.