Automated physical design tuning for database systems has recently become an active area of research and development. Existing tuning tools explore the space of feasible solutions by repeatedly optimizing queries in the input workload for several candidate configurations. This general approach, while scalable, often results in tuning sessions waiting for results from the query optimizer over 90% of the time. In this paper we introduce a novel approach, called Configuration-Parametric Query Optimization, that drastically improves the performance of current tuning tools. By issuing a single optimization call per query, we are able to generate a compact representation of the optimization space that can then produce very efficiently execution plans for the input query under arbitrary configurations. Our experiments show that our technique speeds up query optimization by 30x to over 450x with virtually no loss in quality, and effectively eliminates the optimization bottleneck in existing tuning tools. Our techniques open the door for new, more sophisticated optimization strategies by eliminating the main bottleneck of current tuning tools.