Parallel interference cancellation (PIC) is considered a simple yet effective multiuser detector for direct-sequence code-division multiple-access (DS-CDMA) systems. However, system performance may deteriorate due to unreliable interference cancellation in the early stages. Thus, a partial PIC detector in which partial cancellation factors (PCFs) are introduced to control the interference cancellation level has been developed as a remedy. Although PCFs are crucial, complete solutions for their optimal values are not available. In this paper, we consider a two-stage decoupled partial PIC receiver. Using the minimum bit error rate (BER) criterion, we derive a complete set of optimal PCFs. This includes optimal PCFs for periodic and aperiodic spreading codes in additive white Gaussian channels and multipath channels. Simulation results show that our theoretical optimal PCFs agree closely with empirical ones. Our two-stage partial PIC using derived optimal PCFs outperforms not only a two-stage, but also a three-stage full PIC.