Interactive mining, which is the problem of mining frequent itemsets in a database under different thresholds, is becoming one of the interesting topics in frequent itemsets mining because of needs of practical application. In this paper, we propose a heuristic method for greatly decreasing the number of possible candidates in Poteriori, which is an algorithm based on Apriori for interactive mining. Fewer possible candidates make Poteriori more efficient. Analysis based on an example shows the advantage of our method.