Since the introduction of association rules, many algorithms have been developed to perform the computationally very intensive task of association rule mining. During recent years there has been the tendency in research to concentrate on developing algorithms for specialized tasks, e.g. for mining optimized rules or incrementally updating rule sets. Here we return to the “classic” problem, namely the efficient generation of all association rules that exist in a given set of transactions with respect to minimum support and minimum confidence. From our point of view, the performance problem concerning this task is still not adequately solved. In this paper we address two topics: First of all, today there is no satisfying comparison of the common algorithms. Therefore we identify the fundamental strategies of association rule mining and present a general framework that is independent of any particular approach and its implementation. Based on this we carefully analyze the algorithms. We explain differences and similarities in performance behavior and complete our theoretic insights by runtime experiments. Second, the results are quite surprising and enable us to derive a new algorithm. This approach avoids the identified pitfalls and at the same time profits from the strengths of known approaches. It turns out that it achieves remarkably better runtimes than the previous algorithms.