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Research on query optimization has focused almost exclusively on reducing query execution time, while important qualities such as consistency and predictability have largely been ignored, even though most database users consider these qualities to be at least as important as raw performance. In this paper, we explore how the query optimization process can be made more robust, focusing on the important subproblem of cardinality estimation. The robust cardinality estimation technique that we propose allows for a user- or application-specified trade-off between performance and predictability, and it captures multi-dimensional correlations while remaining space- and time-efficient.