In one embodiment, a coherent optical receiver has an optical detector coupled to a digital processor. The optical detector mixes a received modulated optical signal with a local-oscillator signal to produce a digital measure of the modulated optical signal. The digital processor processes the digital measure using a primary carrier- and data-recovery (CDR) stage and one or more secondary CDR stages serially connected to one another. The processing performed in each secondary CDR stage is decision-directed and uses the symbol estimate generated by the preceding CDR stage to obtain a respective estimate of the carrier-phase offset and a respective symbol estimate. Since each subsequent CDR stage typically improves the accuracies of its estimates compared to those of the preceding CDR stage(s), the receiver has a lower bit-error rate than a receiver employing a single CDR stage.