Rey and Tirole [Handbook of Industrial Organization. Amsterdam: Elsevier (2005)] considered a model in which a monopolist sells to downstream firms using nonlinear contracts. They showed that banning price discrimination fully restores the supplier’s ability to leverage its monopoly power by enabling it to commit not to offer side discounts. I show that the situation changes when the supplier competes against a fringe of less efficient rivals rather than being a monopolist. Then banning price discrimination may cause per-unit prices to fall and welfare to increase. The dominant supplier can take advantage of a strategic bargaining effect: reducing the per-unit price makes the outside option of buying from the fringe less profitable, allowing the dominant supplier to extract more bargaining surplus through the fixed fee.