We introduce TopPI, a new semantics and algorithm designed to mine long-tailed datasets. For each item, and regardless of its frequency, TopPI finds the k most frequent closed itemsets that item belongs to. For example, in our retail dataset, TopPI finds the itemset " nori seaweed, wasabi, sushi rice, soy sauce " that occurrs in only 133 store receipts out of 290 million. It also finds the itemset " milk, puff pastry " , that appears 152,991 times. Thanks to a dynamic threshold adjustment and an adequate pruning strategy, TopPI efficiently traverses the relevant parts of the search space and can be parallelized on multi-cores. Our experiments on datasets with different characteristics show the high performance of TopPI and its superiority when compared to state-of-the-art mining algorithms. We show experimentally on real datasets that TopPI allows the analyst to explore and discover valuable itemsets.