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We investigate carrier synchronization for coherent detection of optical signals encoding 3 and 4 bits/symbol. We consider the effects of laser phase noise and of additive white Gaussian noise (AWGN), which can arise from local oscillator (LO) shot noise or LO-spontaneous beat noise. We identify 8- and 16-ary quadrature amplitude modulation (QAM) schemes that perform well when the receiver phase-locked loop (PLL) tracks the instantaneous signal phase with moderate phase error. We propose implementations of 8- and 16-QAM transmitters using Mach-Zehnder (MZ) modulators. We outline a numerical method for computing the bit error rate (BER) of 8- and 16-QAM in the presence of AWGN and phase error. It is found that these schemes can tolerate phase-error standard deviations of 2.48° and 1.24°, respectively, for a power penalty of 0.5 dB at a BER of 10-9. We propose a suitable PLL design and analyze its performance, taking account of laser phase noise, AWGN, and propagation delay within the PLL. Our analysis shows that the phase error depends on the constellation penalty, which is the mean power of constellation symbols times the mean inverse power. We establish a procedure for finding the optimal PLL natural frequency, and determine tolerable laser linewidths and PLL propagation delays. For zero propagation delay, 8- and 16-QAM can tolerate linewidth-to-bit-rate ratios of 1.8×10-5 and 1.4×10-6, respectively, assuming a total penalty of 1.0 dB.