A soft-floor auction asks bidders to accept an opening price to participate in an ascending auction. If no bidder accepts, lower bids are considered using first-price rules. Soft floors are common despite being irrelevant with standard assumptions. When bidders regret losing, soft-floor auctions are more efficient and profitable than standard optimal auctions. Revenue increases as bidders are inclined to accept the opening price to compete in a regret-free ascending auction. Efficiency is improved since having a soft floor allows for a lower hard reserve price, reducing the frequency of no sale. Theory and experiment confirm these motivations from practice.