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This paper develops a numerical framework for determining whether an ad hoc test is effectively optimal\u2014approximately maximizing a weighted average power criterion for some weights over the alternative and attaining a power en- velope generated by a single weighted average power\u2013maximizing test. Our approach uses nested optimization algorithms to approximate the weight function that makes an ad hoc test\u2019s weighted average power as close as possible to that of a true weighted average power\u2013maximizing test, and we show the surprising result that the rejection probabilities corresponding to the latter form an approximate power envelope for the former. 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