Rare association rules correspond to rare, or infrequent, itemsets, as opposed to frequent ones that are targeted by conventional pattern miners. Rare rules reflect regularities of local, rather than global, scope that can nevertheless provide valuable insights to an expert, especially in areas such as genetics and medical diagnosis where some specific deviations/illnesses occur only in a small number of cases. The work presented here is motivated by the long-standing open question of efficiently mining strong rare rules, i.e., rules with high confidence and low support. We also propose an efficient solution for finding the set of minimal rare itemsets. This set serves as a basis for generating rare association rules.