We present a new algorithm for mining maximal frequent itemsets from a transactional database. The search strategy of the algorithm integrates a depth-first traversal of the itemset lattice with effective pruning mechanisms that significantly improve mining performance. Our implementation for support counting combines a vertical bitmap representation of the data with an efficient bitmap compression scheme. In a thorough experimental analysis, we isolate the effects of individual components of MAFIA including search space pruning techniques and adaptive compression. We also compare our performance with previous work by running tests on very different types of data sets. Our experiments show that MAFIA performs best when mining long itemsets and outperforms other algorithms on dense data by a factor of three to 30.