Partial successive interference cancellation is considered in hybrid DS/FH spread-spectrum multiple-access (SSMA) systems. We first show that the lowest BER attained by employing full interference cancellation in DS/SSMA systems can almost be achieved by employing a partial interference cancellation in hybrid DS/FH systems. The reduction in the number of cancellations translates into an alleviation of correlator speed requirements and a reduction in delays incurred in interference cancellations. The optimal number of frequency slots that minimizes the BER is investigated as a function of the number of interference cancellations. The effect of imperfect power control on the BER is investigated.