A new type of auction has been developed to assign different items to buyers who want to keep their preferences private. This auction is different from others because it only asks bidders for one new bid at a time, adjusts prices transparently, and allows the seller to start with higher prices. Despite these changes, the auction stops after a set time, honest bidding is the best strategy, final prices and revenue depend on buyer values and starting prices, and the auction is efficient if it starts with the seller's values.