The transmission of 8-bit μ-law PCM signals usingM-level weighted QAM (WQAM),M=16, 64 and 256, over Gaussian and Rayleigh fading channels is examined. The weighting process modifies the positions of the QAM constellation points so that the overall distortion in the recovered information-bearing source signal is reduced. The PCM bits are mapped to the WQAM points such that the most significant bits have a lower probability of being in error than the least significant bits. Gray coding of the constellation points is also used. The WQAM systems have been optimised for the same average signal energy per transmitted symbol as for unweighted QAM. Optimised systems have also been derived for the same peak signal energy per symbol. The theoretical and simulation results using speech indicate that 16-level and 256-level WQAM have a gain of up to 3 and 5dB, respectively, over unweighted QAM for the Gaussian channel. The gains due to weighting for 16-level QAM operating over an ideal slow Rayleigh fading channel are up to 5 dB.