An iterative detection and decoding algorithm is explored for a convolutionally coded DS-CDMA system. The optimum decoding strategy is to consider the trellises of all the users simultaneously, but this has exponential complexity in the number of users. We use an iterative +multistage detection scheme combined with the MAP algorithm to reduce the complexity of the receiver without significant performance degradation. The simulation results show that our algorithm consistently outperforms other existing low complexity algorithms. We also provide a framework where the similarities and differences between various algorithms become transparent. Based on this framework, we make a quantitative comparison of the various schemes under investigation.