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(J V k. Approximate algorithms have long been the only available methods for generating Poisson random variates when the mean is large. A new algorithm is developed which is exact, has execution time which is insensitive to the value of the mean, and is valid whenever the mean is greater than ten. This algorithm is compared to the three other algorithms which have been developed recently for generating Poisson variates when the mean is large. Criteria used are set-up time, marginal execution time, memory requirements, and lines of code. New simple tight bounds on Poisson probabilities contribute to the speed of the algorithm, but are useful in a more general context. In addition, a survey of Poisson variate generation algorithms is given