We analyse a bargaining game in which one party, called the buyer, has the option of choosing the sequence of negotiations with other participants, called sellers. When the sequencing of negotiations is confidential and the sellers' goods are highly complementary, efficient, non-dissipative equilibria exist in which the buyer randomizes over negotiation sequences. In these equilibria, the buyer can obtain higher pay-offs than in pure strategy equilibria or in public negotiations. The degree of sequencing uncertainty that maximizes buyer pay-offs is inversely related to the aggregate bargaining power of the sellers.