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To invest effort into any cognitive task, people must be sufficiently motivated. Whereas prior research has focused primarily on how the cognitive control required to complete these tasks is motivated by the potential rewards for success, it is also known that control investment can be equally motivated by the potential negative consequence for failure. Previous theoretical and experimental work has yet to examine how positive and negative incentives differentially influence the manner and intensity with which people allocate control. Here, we develop and test a normative model of control allocation under conditions of varying positive and negative performance incentives. Our model predicts, and our empirical findings confirm, that rewards for success and punishment for failure should differentially influence adjustments to the evidence accumulation rate versus response threshold, respectively. This dissociation further enabled us to infer how motivated a given person was by the consequences of success versus failure.