Conditional asymptotic multi-user efficiency is introduced as a quantitative measure for comparing the performance of multi-user detectors that employ successive interference cancellation (SIC). For a given ordering of user signals, we derive the detector that achieves the maximum asymptotic conditional efficiency for each user among all possible SIC detectors. The optimal ordering that maximizes the asymptotic conditional efficiency at each stage of successive detection is also derived. We extend the concept of maximal asymptotic conditional efficiency detection to the case of joint successive interference cancellation (JSIC), where at each stage of successive detection, the corresponding bit is detected taking into account the interference of the "closest", or nearest, interferer in an ordered set of users. Both detection algorithms proposed are robust against strong correlation of user signals, e.g., in a multi-user system where the user signals are linearly dependent. Simulation results demonstrate that the maximum conditional efficiency approach significantly improves detector performance, particularly at high SNR.