Several studies show that despite experience, many users with basic command knowledge do not progress to an efficient use of complex computer applications. These studies suggest that knowledge of tasks and knowledge of tools are insufficient to lead users to become efficient. To address this problem, we argue that users also need to learn strategies in the intermediate layers of knowledge lying between tasks and tools. These strategies are (a) efficient because they exploit specific powers of computers, (b) difficult to acquire because they are suggested by neither tasks nor tools, and (c) general in nature having wide applicability. The above characteristics are first demonstrated in the context of aggregation strategies that exploit the iterative power of computers. A cognitive analysis of a real-world task reveals that even though such aggregation strategies can have large effects on task time, errors, and on the quality of the final product, they are not often used by even experienced users. We identify other strategies beyond aggregation that can be efficient and useful across computer applications and show how they were used to develop a new approach to training with promising results. We conclude by suggesting that a systematic analysis of strategies in the intermediate layers of knowledge can lead not only to more effective ways to design training but also to more principled approaches to design systems. These advances should lead users to make more efficient use of complex computer systems.