Distributed systems require declarative access to diverse data sources of information. One approach to solving this heterogeneous distributed database problem is based on mediator architectures. In these architectures, mediators accept queries from users, process them with respect to wrappers, and return answers. Wrapper provide access to underlying data sources. To efficiently process queries, the mediator must optimize the plan used for processing the query. In classical databases, cost-estimate based query optimization is an effective method for optimization. In a heterogeneous distributed databases, cost-estimate based query optimization is difficult to achieve because the underlying data sources do not export cost information. This paper describes a new method that permits the wrapper programmer to export cost estimates (cost estimate formulas and statistics). For the wrapper programmer to describe all cost estimates may be impossible due to lack of information or burdensome due to the amount of information. We ease this responsibility of the wrapper programmer by leveraging the generic cost model of the mediator with specific cost estimates from the wrappers. This paper describes the mediator architecture, the language for specifying cost estimates, the algorithm for the blending of cost estimates during query optimization, and experimental results based on a combination of analytical formulas and real measurements of an object database system.