Abstract: Independent auctions are regularly used to sell horizontally differentiated goods. When are these optimal, and what is the optimal mechanism otherwise? We study a Hotelling setting where a seller auctions multiple goods at each end of the interval to risk-neutral buyers with linear transportation costs and private locations. We show that lottery-augmented auctions—which enter some buyers into a lottery over both goods—are optimal whenever independent auctions are not. These auctions are implementable in dominant strategies via two-stage clock auctions with participation fees. Under free disposal, consumer surplus increases as the optimal mechanism transitions from independent to lottery-augmented auctions.