This paper analyzes the design of the Danish milk quota exchange. We focus on the restriction that each producer can only submit a single bid (a quantity and a price limit). We argue that this restriction creates inefficiencies for two reasons. First, a single bid cannot express a buyer's downward sloping demand curve (the aggregation effect). Second, the buyers minimize the risk of foregoing profitable trade by submitting their average valuation rather than their marginal valuation of quota (the uncertainty effect). We use data from the (multiple bids) Ontario milk quota exchange, to evaluate the empirical impact of a single bid restriction.