Previous results have shown that high rate codes tend to yield a lower average bit-error rate than low rate codes when employing a minimum mean-square error (MMSE) receiver for a direct-sequence code-division multiple-access (CDMA) system in either an additive white Gaussian noise channel or a flat Rayleigh fading channel. we consider the use of larger signal constellations with both trellis-coded modulation and bit-interleaved coded modulation (BICM) to determine if further gains can be achieved in either the Rayleigh or Ricean fading channel. The average bit-error probability is derived for both coding schemes using the general Ricean fading channel model, based upon the common assumptions of infinite interleaving, perfect channel state information, and optimal MMSE receiver coefficients. New bounds are presented for BICM with 8-PSK and 16-QAM symbols, which take advantage of the symmetries inherent in the signal constellations with Gray code mapping. In addition, simulation results are presented which show the important effect a finite interleaving delay constraint has on the comparison of various codes. The results show that there are cases when coded modulation does yield a significant improvement in performance for a CDMA system using an MMSE receiver, compared to standard convolutional coding. However, the best coding strategy depends upon several factors, including the nature of the fading process (Rayleigh or Ricean), the operating signal-to-noise ratio, the interleaving delay constraint, the time-variability of the channel, the number of users in the system, and the severity of the near-far problem.