Convolutional spreading CDMA with cyclic prefix (CS-CDMA/CP) enables multiuser interference-free (MUI-free) transmission over multipath downlink channels with the use of zero correlation zone (ZCZ) codes. However, MUI-free transmission is guaranteed only when the data length D, channel delay L, and ZCZ length Z satisfy Z+1 ≥ D + L. In this paper, we consider the situation that MUI-free transmission is not realized inevitably because of excessive multipath delays or deliberately because of the necessity to get a higher bandwidth efficiency, clarify the structure of MUI in the CS-CDMA/CP system employing M-ZCZ codes, and propose iterative partial multiuser detection (IPMUD). The detection is implemented at symbol-level (after despreading) and the number of users jointly considered can be adjusted flexibly to offer a tradeoff between system performance and receiver complexity. The performance of the proposed scheme is verified numerically by density evolution approach and BER simulations. The CS-CDMA/CP system with IPMUD is shown to be much less complex than the DS-CDMA system with Wang and Poor's turbo MUD receiver and to be less complex and better, in terms of bit error rate (BER) performance, than the DS-CDMA system with iterative chip-wise equalization receivers.