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An approach to successive interference cancellation is presented that exploits the structure of the combined signal constellation in a multiuser system. The asymptotic conditional efficiency of a successive detector is defined, based on the conditional probability of error at high signal-to-noise ratio (SNR), as a quantitative measure for evaluating detector performance at each stage of successive detection. The joint successive interference canceller (JSIC) that jointly detects consecutive users in an ordered set is proposed as an improvement over the conventional successive interference canceller (SIC). The maximal asymptotic conditional efficiency successive interference canceller (MACE-SIC) and its JSIC equivalent (MACE-JSIC) are also derived as the multiuser detectors that achieve the highest asymptotic conditional multiuser efficiency at each stage of successive detection among all possible SIC and JSIC detectors, respectively, given any particular ordering of user signals. The ordering of users achieving the highest asymptotic conditional efficiency at each stage of successive detection is derived. Performance bounds based on the signal constellation structure are derived to quantify the gain of the MACE-JSIC detector compared to the MACE-SIC detector.