We describe here a general approach for rare itemset mining. While mining literature has been almost exclu- sively focused on frequent itemsets, in many practical sit- uations rare ones are of higher interest (e.g., in medical databases, rare combinations of symptoms might provide useful insights for the physicians). Based on an examina- tion of the relevant substructures of the mining space, our approach splits the rare itemset mining task into two steps, i.e., frequent itemset part traversal and rare itemset listing. We propose two algorithms for step one, a na?ive and an optimized one, respectively, and another algorithm for step two. We also provide some empirical evidence about the performance gains due to the optimized traversal.