I analyze cliff discounts when an incumbent monopolist faces competition from a competitor that can compete for a portion (but not all) of the market, and compare them with both simple pricing and pricing formulas in which the incumbent can cut prices just in the competitive portion of the market. The optimal cliff discount does not require exclusivity by the buyer. By leaving a portion of the market to the competitor, the incumbent gives it the choice between accepting its allocated share at a high price and offering deep discounts for any increase in market share. The optimal contract allows the competitor to earn higher profits by charging a high price for its allocated share, which in turn allows the incumbent to charge a high price. Average prices are higher with the cliff discount than with pricing that targets price cuts to the competitive segment. The model can apply to bundled discounts for multiple products as well as all-units discounts on a single product.