Interesting patterns often occur at varied levels of support. The classic association mining based on a uniform minimum support, such as Apriori, either misses interesting patterns of low support or suffers from the bottleneck of itemset generation caused by a low minimum support. A better solution lies in exploiting support constraints, which specify what minimum support is required for what itemsets, so that only the necessary itemsets are generated. We present a framework of frequent itemset mining in the presence of support constraints. Our approach is to "push" support constraints into the Apriori itemset generation so that the "best" minimum support is determined for each itemset at runtime to preserve the essence of Apriori. This strategy is called Adaptive Apriori. Experiments show that Adapative Apriori is highly effective in dealing with the bottleneck of itemset generation.