We introduce a new algorithm for mining sequential patterns. Our algorithm is especially efficient when the sequential patterns in the database are very long. We introduce a novel depth-first search strategy that integrates a depth-first traversal of the search space with effective pruning mechanisms. Our implementation of the search strategy combines a vertical bitmap representation of the database with efficient support counting. A salient feature of our algorithm is that it incrementally outputs new frequent itemsets in an online fashion. In a thorough experimental evaluation of our algorithm on standard benchmark data from the literature, our algorithm outperforms previous work up to an order of magnitude.