Simon?s (1955) famous paper was one of the first to cast doubt on the validity of rational choice theory; it has been supplemented by many more papers in the last three and a half decades. Nevertheless, rational choice theory plays a crucial role in classical and neoclassical economic theory, which presumes a completely rational agent. The central points characterizing such an agent are: (1) The agent uses all the information that is given to him. (2) The agent has clear preferences with respect to the results of different actions. (3) The agent has adequate competences to optimize his decisions. As an alternative to this conception, Simon (1955) himself suggests the concept of ?bounded rationality?. In this context, Simon (1956) discusses a principle, which he names the ?satisficing principle? (for explanations with respect to this notion cf. Gigerenzer & Todd 1999, p. 13). It assumes that, instead of searching for an optimal action, the search for an action terminates if an alternative has been found that satisfies a given ?aspiration level?. It will be demonstrated that although the satisficing principle is nothing but a heuristic, there is a mathematical optimization at work when aspiration levels are used in this kind of problems. The question about the optimal aspiration level can be posed. Optimization within the framework of bounded rationality is possible. However, the way in which such an optimization can be achieved is very simple: Optimal thresholds in binary sequential decisions rest with the median.