Association rules discovery is one of the most important tasks in Knowledge Discovery in Data Bases. Since the initial APRIORI algorithm, many efforts have been done in order to develop efficient algorithms. It is well known that APRIORI-like algorithms within the (unsatisfying) support/ confidence framework may produce huge amounts of rules and thus one of the most important steps in association rules discovery is nowadays the evaluation and interpretation of their interestingness. Thus there has been substantial works that addressed the problem of association rules interestingness and many interestingness measures have been defined and used in order to find the best rules in a post-processing step. Measures provide numerical information on the quality of a rule and a rule A ! B is said "of quality" if its evaluation by a measure is greater than a user defined threshold. These measures can be studied as functions of the number of counter-examples of rules. In this paper we present three modelings of counter-examples and examine the consequences of such modelizations on two important desired properties of association rules interestingness measures, that are the decrease with the number of counterexamples and the tolerance to the apparition of the first counterexamples. We here present results for ten well known measures.