Prior work in hardware prefetching has focused mostly on either predicting regular streams with uniform strides, or predicting irregular access patterns at the cost of large hardware structures. This paper introduces the Variable Length Delta Prefetcher (VLDP), which builds up delta histories between successive cache line misses within physical pages, and then uses these histories to predict the order of cache line misses in new pages. One of VLDP's distinguishing features is its use of multiple prediction tables, each of which stores predictions based on a different length of input history. For example, the first prediction table takes as input only the single most recent delta between cache misses within a page, and attempts to predict the next cache miss in that page. The second prediction table takes as input a sequence of the two most recent deltas between cache misses within a page, and also attempts to predict the next cache miss in that page, and so on with additional tables. Longer histories generally yield more accurate predictions, so VLDP prefers to make predictions based on the longest history table that has a matching entry.