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A direct-sequence spread-spectrum multiple-access bit-error probability analysis is developed using large-deviations theory. Let m denote the number of interfering spread-spectrum signals and let n denote the signature sequence length. Then the large deviations limit is as n to infinity with m fixed. A tight asymptotic expression for the bit-error probability is proven, and in addition, recent large-deviations results with the importance sampling Monte Carlo estimation technique are applied to obtain accurate and computationally efficient estimates of the bit-error probability for finite values of m and n. The large-deviations point of view is compared also to the conventional asymptotics of central limit theory and the associated Gaussian approximation. The Gaussian approximation is accurate and the ratio m/n is moderately large and all signals have roughly equal power. In the near/far situation, however, the Gaussian approximation is quite poor. In contrast, large-deviations techniques are more accurate in the near/far situation, and it is here that these methods provide some important practical insight.