The relationship between reward value and cognitive performance is often thought to be curvilinear, shaped like an inverted U. Moderately valuable rewards should facilitate, but extremely valuable rewards should harm, performance. Despite the popularity of this idea, the dose–response relationship between reward value and cognitive performance is not yet well-understood. Here we present a set of experiments (total N = 254) that examine the effects of monetary reward (no reward, medium reward, extreme reward) on task-switching performance. Overall, more valuable rewards led to better performance. Yet, when physical reward cues were present (i.e., when the money at stake was placed on the table), we observed the predicted inverted-U-shaped relationship. Together, our results suggest that (a) people are often able to maintain good cognitive performance when the stakes are high, and that (b) physical reward cues may play a key role in triggering ‘choking under pressure’.