Each firm has one unit to sell of a differentiated product and each consumer has demand for one unit. Consumers queue at the firms, inspect their products if they get the turn, and choose whether to buy or not. We study how selling constraints, which refer to the possible inability of firms to attend to all the buyers who may queue at their premises, affect the equilibrium price and social welfare. Efficient pricing typically involves a positive markup. A higher price, on the one hand, increases the value of trade (because only trades generating positive surplus are consummated) and, on the other hand, reduces the quantity of trade (because fewer buyers can afford paying a higher price). We show that equilibrium markups are inefficiently high except in the limiting situation of no selling constraints, in which case the equilibrium markup is efficient. Thus, selling constraints constitute a source of market power.