Multiple access interference (MAI) is a significant limiting factor in the performance of direct sequence code division multiple access (DS-CDMA) systems. Various multiuser detection techniques have been developed to combat the effects of MAI. These detection techniques either assume the knowledge of all the users in the system (conventional) or assume the knowledge of the user of interest only (blind). Due to the limitations of the blind algorithms in the presence of a large number of interferers, there is a significant performance gap between these two classes of detectors. Additionally, in practice, the receiver could have only partial knowledge of the interference. In this paper, we develop a new class of detectors, partially blind multiuser detectors, that use information about a subset of interferers and bridge the performance gap between the blind and the conventional multiuser detectors.