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Statistical selection procedures can identify the best of a finite set of alternatives, where “best ” is defined in terms of the unknown expected value of each alternative’s simulation output. One effective Bayesian approach allocates samples sequentially to maximize an approximation to the expected value of information (EVI) from those samples. That existing approach uses both asymptotic and probabilistic approximations. This paper presents new EVI sampling allocations that avoid most of those approximations, but that entail sequential myopic sampling from a single alternative per stage of sampling. We compare the new and old approaches empirically. In some scenarios (a small, fixed total number of samples, few systems to be compared), the new greedy myopic procedures are better than the original asymptotic variants. In other scenarios (with adaptive stopping rules, medium or large number of systems, high required probability of correct selection), the original asymptotic allocations perform better.