In this paper, we introduce self-tuning histograms. Although similar in structure to traditional histograms, these histograms infer data distributions not by examining the data or a sample thereof, but by using feedback from the query execution engine about the actual selectivity of range selection operators to progressively refine the histogram. Since the cost of building and maintaining self-tuning histograms is independent of the data size, self-tuning histograms provide a remarkably inexpensive way to construct histograms for large data sets with little up-front costs. Self-tuning histograms are particularly attractive as an alternative to multi-dimensional traditional histograms that capture dependencies between attributes but are prohibitively expensive to build and maintain. In this paper, we describe the techniques for initializing and refining self-tuning histograms. Our experimental results show that self-tuning histograms provide a low-cost alternative to traditional multi-...