Cognitive radio is promising in improving spectrum efficiency by enabling unlicensed users to access to the licensed spectrum. Spectrum auction is perceived as a potential way to realize it. Primary users (PUs) act as sellers selling unused spectrum bands and secondary users (SUs) act as buyers who intend to get spectrum bands from PUs. In situations where multiple PUs and SUs exist, double auction is a paradigm to assign spectrum. Efficiency and economic robustness are considered two essential properties in the model. Previous work often employ bid-independent uniform pricing to maintain economic robust at the substantial cost of efficiency. In this paper, we investigate the tradeoff between efficiency and robustness. We propose DIPA, a DIscriminatory Pricing double Auction for spectrum, in which bidders are charged of varying prices for the same item they purchase. We demonstrate that DIPA is robust and improves efficiency largely over the previous design.