A pattern database is a heuristic function stored as a lookup table which stores the lengths of optimal solutions for instances of subproblems. All previous pattern databases had a distinct entry in the table for each subproblem instance. In this paper we investigate compressing pattern databases by merging several adjacent entries into one, thereby allowing the use of pattern databases that exceed available memory in their uncompressed form. We show that since adjacent entries are highly correlated, much of the information is preserved. Experiments on the sliding tile puzzles and the 4-peg Towers of Hanoi puzzle show that, for a given amount of memory, search time is reduced by up to 3 orders of magnitude by using compressed pattern databases.