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If a Costas loop is forced to have a relatively wide bandwidth, for example, to track phase variation due to platform motion, binary phase-shift keying (BPSK) demodulator performance is significantly degraded. However, if the data bits were known, the Costas loop would become equivalent to a phase-locked loop, which has approximately a 6-dB lower tracking threshold for the same loop bandwidth. A delayed-bit estimation algorithm with a recursive structure similar to the Viterbi algorithm is described. The memory in the tracking loop is exploited to correct preliminary bit decisions, as a means of realizing most of this theoretical threshold reduction. Experimental results for a practical digital implementation of the new algorithm for a 50-bit/s data rate and a 20-Hz loop noise bandwidth show a 4-dB improvement in demodulator threshold.