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In this work we study the mining of top-K frequent closed itemsets, a recently proposed variant of the classical problem of mining frequent closed itemsets where the support threshold is chosen as the maximum value sufficient to guarantee that the itemsets returned in output be at least K. We discuss the effectiveness of parameter K in controlling the output size and develop an efficient algorithm for mining top-K frequent closed itemsets in order of decreasing support, which exhibits consistently better performance than the best previously known one, attaining substantial improvements in some cases. A distinctive feature of our algorithm is that it allows the user to dynamically raise the value K with no need to restart the computation from scratch.