The traditional association rule mining framework produces many redundant rules. The extent of redundancy is a lot larger than previously suspected. We present a new framework for associations based on the concept of closed frequent itemsets. The number of non-redundant rules produced by the new approach is exponentially (in the length of the longest frequent itemset) smaller than the rule set from the traditional approach. Experiments using several “hard” as well as “easy” real and synthetic databases confirm the utility of our framework in terms of reduction in the number of rules presented to the user, and in terms of time.