Although the current shortage of radio spectrum is usually attributed to the scarcity of spectrum, it is due to the inefficiency of legacy radio technologies and old systems of spectrum management. Regulatory reforms are being proposed to assign exclusive rights to spectrum, but such "market-oriented" allocation would be harmful because the spectrum is not a property but a protocol by which information is carried. New packet radio technologies enable efficient communications by sharing a wide band without licenses. However, it is difficult to relocate spectrum by persuading incumbents to give back their spectrum. Therefore we propose reverse auctions by which the government buys back spectrum from incumbents as an optional mechanism for spectrum relocation. The equilibrium price of this reverse auction will be much cheaper than that of ordinary spectrum auctions, because the former price will be close to the value of the band that is used least efficiently if the auction is competitive.