We analyze algorithms that, under the right circumstances, permit efficient mining for frequent itemsets in data with tall peaks (large frequent itemsets). We develop a family of level-by-level peak-jumping algorithms, and study them using a simple probability model. The analysis clarifies why the jumping idea sometimes works well, and which properties the data needs to have for this to be the case. The link with Max-Miner arises in a natural way and the analysis makes clear the role and importance of each major idea used in this algorithm.