In a typical mobile communications channel, the multiple access interference (MAI) experienced by any user in a multiuser CDMA system will be complex-valued due to independent phase offsets between signals received from different users. In addition, complex spreading codes may also be employed, in which case MAI is complex-valued even without phase offsets. This paper shows that complex MAI substantially alters the single-user relationship between BPSK and QPSK modulation, in which QPSK offers twice the bandwidth efficiency of BPSK without sacrificing BER versus Eb/N0 performance. It is shown both analytically and through simulations that it is possible to adjust system parameters to achieve identical system bandwidth efficiency and BER performance in BPSK and QPSK systems using the conventional detector. The performance of the well-known successive interference canceller and decorrelating detector are also examined.