When buyers choose the order in which they bargain with suppliers of known characteristics, prices are determined jointly by bargaining power and competitive intensity (the outside option to bargain with rival suppliers). Bargaining power becomes less important to the outcome as competition intensifies; prices fall to marginal cost in the limit. With positive visit costs and weak competition, some buyer power is necessary for trade. Incomplete buyer power may lead to inefficient choice of bargaining order. The robustness of ordered bargaining to the possibility of price posting and auctions, and welfare properties of these alternative pricing institutions are also explored.