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In this paper, a combined approach is taken to the multiple access problem, by integrating the interference reduction properties of the spreading code (signature sequence) with an algorithm for collision resolution (CRA). This approach makes specific use of the properties of direct-sequence (DS) signaling to aid in making the CRA more efficient. An accurate throughput analysis is performed, and an arbitrarily tight lower bound to the maximum stable throughput is derived. An approximation is developed for an important quantity that arises in DS/SSMA systems, namely the probability of exactly m users suffering packet error given that k users transmit simultaneously; this approximation has satisfactory accuracy for all values of M and k and its computational complexity remains linear in m and k. Finally, a procedure is proposed for estimating the level of channel traffic, by making use of the nature of the signaling involved.