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In this paper, we present a simple method of selecting the partial cancellation factors (PCFs) for a two-stage, hard-decision, partial parallel interference cancellation (PPIC) detector for direct-sequence code-division multiple access (DS-CDMA) systems. Using Price's theorem, we derive a range of the optimal PCF for each PPIC stage in multipath fading environments, where the lower and upper bounds can be explicitly calculated from the processing gain and the number of active users of the DS-CDMA system considered. Computer simulation results show that, using the average of the lower and upper bounds as the PCF for each PPIC stage, the bit error rate (BER) performance closely approximates that of the real optimal PCFs. Moreover, a multistage PPIC detector using the proposed PCFs in the first two stages achieves its BER performance limit with fewer stages. That is, the proposed PCF selection method reduces the complexity of a PPIC detector and provides the same BER performance. This makes the proposed PCFs attractive for use in PPIC receivers in DS-CDMA systems.