We introduce a new type of OCDMA/OCDMA for oversaturated channels, by displacing in time the orthogonal signature sets of the users. A displacement by an integer multiple of a chip period considerably improves the performance of iterative detection of the user data, as compared to quasi-orthogonal sequences (QOS) and conventional random O/O sequences. An additional displacement by half a chip period reduces the variance of the cross correlation between the. users of the two sets by up to 50%, and results in an additional performance improvement for square root cosine rolloff chip pulses. This improved O/O system can accommodate a number of Users equal to twice the spreading gain N, when N greater than or equal to 32. For a practical rolloff of 25% and N = 128, the acceptable channel overload Can almost be tripled with improved O/O as compared to conventional O/O.