This paper presents a low-complexity multiuser decoding technique that can be implemented in real time for a convolutionally coded direct sequence code division multiple access (DS-CDMA) system. The main contribution, denoted here as the iterative prior update (IPU), consists of iterative interference cancellation and prior updates on sequences of coded bits combined with M-algorithm and list decoding. We illustrate performance gains over other low-complexity sequence detection and decoding strategies and argue that the algorithm converges within a few iterations and requires only a small size buffer for keeping track of the priors along iterations. The fact that the we can use existing available architectures for Viterbi decoding with slight modifications and can meet the real-time processing constraints makes the IPU algorithm an attractive alternative for cellular systems.