In classical association rules mining, a minimum support threshold is assumed to be available for mining frequent itemsets. However, setting such a threshold is typically hard. If the threshold is set too high, nothing will be discovered; and if it is set too low, too many itemsets will be generated, which also implies inefficiency. In this paper, we handle a more practical problem, roughly speaking, it is to mine the N k-itemsets with the highest support for k up to a certain kmax value. We call the results the N-most interesting itemsets. Generally, it is more straightforward for users to determine N and kmax. This approach also provides a solution for an open issue in the problem of subspace clustering. However, with the above problem definition without the support threshold, the subset closure property of the apriori-gen algorithm no longer holds. We propose three new algorithms, LOOPBACK, BOLB, and BOMO, for mining N-most interesting itemsets by variations of the FP-tree approach. Experiments show that all our methods outperform the previously proposed Itemset-Loop algorithm.