We are developing an object-oriented real-time database system that includes a relationally complete query language. Unlike conventional query optimizers, our optimizer estimates the actual time to execute a query, rather than a rough average cost estimate. For predictability the optimizer must make reliable estimates of the time to execute a query. This requires index structures that are predictable. Furthermore, our data model is object-oriented, which is used for overloading queries with respect to tradeoffs between execution time and quality. Such performancepolymorphic queries have particular optimization problems.