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Tardos has proposed a randomized fingerprinting code that is provably secure against collusion attacks. We revisit his scheme and show that it has significantly better performance than suggested in the original paper. First, we introduce variables in place of Tardos' hard-coded constants and we allow for an independent choice of the desired false positive (FP) and false negative (FN) error rates. Following through Tardos' proofs with these modifications, we show that the code length can be reduced by more than a factor of two in typical content distribution applications where high FN rates can be tolerated. Second, we study the statistical properties of the code. Under some reasonable assumptions, the accusation sums can be regarded as Gaussian-distributed stochastic variables. In this approximation, the desired error rates are achieved by a code length twice shorter than in the first approach. Overall, typical FP and FN error rates may be achieved with a code length approximately five times shorter than in the original construction.