Locality Sensitive Hashing (LSH) is widely used for efficient retrieval of candidate matches in very large audio, video, and image systems. However, extremely large reference databases necessitate a guaranteed limit on the memory used by the table lookup itself, no matter how the entries crowd different parts of the signature space, a guarantee that LSH does not give. In this paper, we provide such guaranteed limits, primarily through the design of the LSH bands. When combined with data-adaptive bin splitting (needed on only 0.04%% of the occupied bins), this approach provides the required guarantee on memory usage. At the same time, it avoids the reduced recall that more extensive use of bin splitting would give.