Many previous studies have found that an increase in phasic or tonic alertness impairs cognitive control, even though overall response times are decreased. This counterintuitive pattern of behavior is still poorly understood. Using a computational model, we show that the behavioral pattern follows directly from two simple and well-supported assumptions: increased alertness reduces the time needed for stimulus encoding; and cognitive control takes time to develop. The simulation results suggest that, although the arousal system and cognitive control system may be anatomically distinct, their effects on information processing may interact to produce a seemingly complicated pattern of behavior.