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The allowable load in oversaturated CDMA systems is investigated, so that the uncoded performance with multistage successive interference cancellation (m-SIC) remains close to the single user bound. As oversaturated systems, we consider pseudo-noise CDMA (PN), pseudo noise/ orthogonal CDMA (PN/O) and orthogonal/orthogonal CDMA (O/O). For O/O, we make a distinction between scrambled O/O (s-O/O) and overall-permuted O/O (o-O/O). Because of the special structure of the O/O signature set, the intrinsic delay of m-SIC is drastically reduced in O/O as compared to PN and PN/O. For all systems, it is found that the achievable acceptable overload increases with the spreading factor. The o-O/O system outperforms s-O/O, while PN/O is inferior to o-O/O. Both O/O systems and the PN/O system clearly outperform PN.