One of the most compelling characteristics of controlled processing is our limitation to exercise it. These limitations have become a fundamental concept in general theories of cognition that explain idiosyncrasies of human performance in terms of rational adaptations to a) the limited number of control-dependent tasks that can be executed simultaneously and b) constraints on the amount of cognitive control that can be allocated to a single task. However, this leaves open the question of why such constraints would exist in the first place. In this talk I will explore the hypothesis that the bounds of cognitive control reflect, at least in part, an optimal solution to two fundamental computational dilemmas in neural network architectures. Using neural network simulations and behavioral experiments I will first demonstrate that neural architectures are subject to a tradeoff between learning efficiency that is promoted through the use of shared task representations, on the one hand, and multitasking capability that is achieved through the separation of task representations, on the other hand. From this perspective, limitations on the number of control-demanding tasks that can be executed at the same time may reflect a preference of the neural system to learn tasks more quickly. As a consequence, executing multiple control-demanding tasks may only occur in serial, through flexible switching between tasks. The serial execution of tasks, however, gives rise to another tradeoff known as the stability-flexibility dilemma: allocating more control to a task results in greater activation of its neural representation but also in greater persistence of this activity upon switching to a new task, yielding switch costs. I will demonstrate that constraints on the amount of cognitive control allocated to a single task can reflect an optimal solution to this dilemma. I will argue that the study of computational dilemmas in neural systems may hold promise to uncover normative explanations for the seemingly irrational constraints on cognitive control, as well as human cognition in general.