The key point of this paper is that, in frequent pattern mining, the most appropriate way of exploiting monotone constraints in conjunction with frequency is to use them in order to reduce the problem input together with the search space. Following this intuition, we introduce ExAMiner, a level-wise algorithm which exploits the real synergy of anti-monotone and monotone constraints: the total benefit is greater than the sum of the two individual benefits. ExAMiner generalizes the basic idea of the preprocessing algorithm ExAnte, embedding such ideas at all levels of an Apriori-like computation. The resulting algorithm is the generalization of the Apriori algorithm when a conjunction of monotone constraints is conjoined to the frequency anti-monotone constraint. Experimental results confirm that this is, so far, the most efficient way of attacking the computational problem in analysis.