In this paper, we present an improved version of partial parallel interference cancellation (PPIC), called variancereduced PPIC (VRPPIC), for multicarrier code division multiple access uplink systems. The VRPPIC detector is a combination of the PPIC receiver and a new bit estimator, where a simplified realization is derived for the main PPIC operations and soft decisions from PPIC are linearly combined by the bit estimator using appropriate weighting factors (derived from the PPIC weighting factors) to reduce the conditional variance of the final signal estimate. Also, we derive an optimal weighting factor (OWF) selection algorithm for VRPPIC based on minimizing a monotonically increasing conditional variance function. The derived OWFs for all the interference cancellation stages are equal and can easily be obtained from a linear function of the number of active users. Simulation results show that VRPPIC with the proposed OWFs significantly outperforms VRPPIC (or PPIC) with randomly selected weighting factors in multipath Rayleigh fading channels.