Successive interference cancellation (SIC) refers to a family of low-complexity multiuser detection methods for direct-sequence code-division multiple-access systems. The performance of multistage SIC depends on the decision function used in the interference cancellation iterations, e.g., hard, soft, or linear decision functions. Due to error propagation, multistage SIC with hard data bit decisions may perform more poorly than multistage SIC with linear or soft decision functions. We propose and analyze a family of generalized unit-clipper bit decision functions that better combine linear and hard decisions. Performance within 0.4 dB of the single-user bound can be obtained. We then make robust the above soft-decision SIC to time-delay errors as large as half a PN chip and evaluate its performance.