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We present the design and analysis of the first fully expressive, iterative combinatorial exchange (ICE). The exchange incorporates a tree-based bidding language (TBBL) that is concise and expressive for CEs. Bidders specify lower and upper bounds in TBBL on their value for different trades and refine these bounds across rounds. These bounds allow price discovery and useful preference elicitation in early rounds, and allow termination with an efficient trade despite partial information on bidder valuations. All computation in the exchange is carefully optimized to exploit the structure of the bid-trees and to avoid enumerating trades. A proxied interpretation of a revealed-preference activity rule, coupled with simple linear prices, ensures progress across rounds. The exchange is fully implemented, and we give results demonstrating several aspects of its scalability and economic properties with simulated bidding strategies.