We design truthful double spectrum auctions where multiple parties can trade spectrum based on their individual needs. Open, market-based spectrum trading motivates existing spectrum owners (as sellers) to lease their selected idle spectrum to new spectrum users, and provides new users (as buyers) the spectrum they desperately need. The most significant challenge is how to make the auction economic-robust (truthful in particular) while enabling spectrum reuse to improve spectrum utilization. Unfortunately, existing designs either do not consider spectrum reuse or become untruthful when applied to double spectrum auctions. We address this challenge by proposing TRUST, a general framework for truthful double spectrum auctions. TRUST takes as input any reusability-driven spectrum allocation algorithm, and applies a novel winner determination and pricing mechanism to achieve truthfulness and other economic properties while significantly improving spectrum utilization. To our best knowledge, TRUST is the first solution for truthful double spectrum auctions that enable spectrum reuse. Our results show that economic factors introduce a tradeoff between spectrum efficiency and economic robustness. TRUST makes an important contribution on enabling spectrum reuse to minimize such tradeoff.