Some existing notions of redundancy among association rules allow for a logical-style characterization and lead to irredundant bases of absolutely minimum size. One can push the intuition of redundancy further and find an intuitive notion of interest of an association rule, in terms of its "novelty" with respect to other rules. Namely: an irredundant rule is so because its confidence is higher than what the rest of the rules would suggest; then, one can ask: how much higher? We propose to measure such a sort of "novelty" through the confidence boost of a rule, which encompasses two previous similar notions (confidence width and rule blocking, of which the latter is closely related to the earlier measure "improvement"). Acting as a complement to confidence and support, the confidence boost helps to obtain small and crisp sets of mined association rules, and solves the well-known problem that, in certain cases, rules of negative correlation may pass the confidence bound. We analyze the properties of two versions of the notion of confidence boost, one of them a natural generalization of the other. We develop efficient algorithmics to filter rules according to their confidence boost, compare the concept to some similar notions in the bibliography, and describe the results of some experimentation employing the new notions on standard benchmark datasets. We describe an open-source association mining tool that embodies one of our variants of confidence boost in such a way that the data mining process does not require the user to select any value for any parameter.