Countermanding an action is a fundamental form of cognitive control. In a saccade countermanding task, subjects are instructed that, if a stop signal appears shortly after atarget, they are to maintain fixation rather than to make a saccade to the target. In recentyears, recordings in the frontal eye fields and superior colliculus of behaving non-humanprimates have found correlates of such countermanding behavior in movement and fixationneurons. In this work, we extend a previous neural network model of countermanding toaccount for the high pre-target activity of fixation neurons. We propose that this activityreflects the functioning of control mechanisms responsible for optimizing performance. Wedemonstrate, using computer simulations and mathematical analysis, that pre-targetfixation neuronal activity supports countermanding behavior that maximizes reward rateas a function of the stop signal delay, fraction of stop signal trials, intertrial interval,duration of timeout, and relative reward value. We propose experiments to test thesepredictions regarding optimal behavior.