IN selling bills, the U.S. Treasury employs a discriminatory auction. The Treasury awards bills in the amounts and at the prices bid, beginning with the highest price and proceeding to consecutively lower prices, until the issue is allotted. A common practice -of bidders in the weekly auctions is to strip-bid; that is, to bid approximately equal amounts around the anticipated stop-out price, the lowest price at which bills are awarded. Although a number of writers have evaluated the revenue generating capabilities of the discriminatory auction, only one, Vernon Smith, attempted to do so ,through the specification of a utility maximizing model of the bidding decision.' Despite the prevalence of multiple price bidding in practice, however, Smith posited the selection of a single price bid. This paper examines the theoretical and empirical aspects of the multiple price bid in Treasury bill auctions. Section I briefly describes the weekly auctions. Section II presents a model of the bidding decision which shows that, in general, multiple price bids are optimal. Multiple price bids are examined empirically in section III. Bids that are efficient in a mean-variance sense are derived from the forecasts of actual bidders.2 In a comparison covering 75 auctions, the efficient bids had higher mean profit and lower standard deviations of profit than the dealers' actual bids on an ex post as well as ex ante basis.