Association rule mining is well-known to depend heavily on a support threshold parameter, and on one or more thresholds for intensity of implication; among these measures, confidence is most often used and, sometimes, related alternatives such as lift, leverage, improvement, or all-confidence are employed, either separately or jointly with confidence. We remain within the support-and-confidence framework in an attempt at studying complementary notions, which have the goal of measuring relative forms of objective novelty or surprisingness of each individual rule with respect to other rules that hold in the same dataset. We measure novelty through the extent to which the confidence value is robust, taken relative to the confidences of related (for instance, logically stronger) rules, as opposed to the absolute consideration of the single rule at hand. We consider two variants of this idea and analyze their logical and algorithmic properties. Since this approach has the drawback of requiring further parameters, we also propose a framework in which the user sets a single parameter, of quite clear intuitive semantics, from which the corresponding thresholds for confidence and novelty are computed.