The complexity of the optimal decoding for vector quantization (VQ) in code-division multiple access (CDMA) communications prohibits implementation. It was recently shown in [1] that a suboptimal scheme that combines a soft-output multiuser detector and individual VQ decoders provides a flexible tradeoff between decoder's complexity and performance. The work in [1], however, only considers an AWGN channel model. This paper extends the technique in [1] to a frequency-selective Rayleigh fading channel. Simulation results indicate that such a suboptimal decoder also performs very well over this type of channel.