In recent years, combining multiuser detection (MUD) and channel decoding has received considerable attention. The maximum a posteriori (MAP) criterion-based iterative multiuser detector greatly improves the system performance and can approach the performance of single-user coded systems. However, its complexity increases exponentially with the number of users and can become prohibitive for systems with a medium-to-large number of users. In this paper, a reduced complexity MAP-based iterative MUD based on the use of a soft sensitive bits algorithm is proposed for coded multicarrier code-division multiple-access systems. It is shown that it can greatly reduce the computational complexity with a minimal penalty in performance compared to the conventional optimal scheme.