This paper deals with the development of a new family of simplification procedures that can be applied to those communications problems analyzed using the Bayesian formulation. Specifically, our work focuses on near-optimum Bayesian multiuser detectors for synchronous DS/CDMA systems. The complexity of the theoretical Bayesian approach grows exponentially with both the number of active users and the number of symbols received, constituting, this way, not a viable detection solution. Therefore, the development of suboptimal algorithms by making use of a new set of simplifications strategies becomes a crucial issue to be addressed. In this work, a global framework for multiuser Bayesian equalization is first established by developing a general algorithm suitable for blind (non-data-aided) communications scenarios. Afterwards, a group of simplification techniques is introduced and, finally, the performance is evaluated and compared to that of the most well-known traditional multiuser detectors.