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We investigate the strategic effects of all‐units discounts (AUDs) used by a dominant firm in the presence of a capacity‐constrained rival. Due to the limited capacity of the rival, the dominant firm has a captive portion of the buyer's demand for the single product. As compared to linear pricing, the dominant firm can use AUDs to go beyond its captive portion by tying its captive demand with part of the competitive demand and partially foreclose its small rival. When the rival's capacity level is well below relevant demand, AUDs reduce the buyer's surplus.