We examine a quantity competition among branded and nonbranded firms. The market comprises two consumer segments: one purchases only branded products (the high-end market), while the other segment's consumers purchase less expensive products (the low-end market). When branded firms take actions sequentially, we show that the branded leader has an incentive to restrict its quantity to avoid entering the low-end market. As the follower recognizes this incentive, it can restrict the leader by implementing a quantity constraint, which is affected by the number of nonbranded firms. We find that both the branded leader and follower could benefit from the nonbranded firms and that the leader prefers to have more nonbranded firms in the market than the follower does. Furthermore, we show that the free entry of nonbranded firms could negatively affect total surplus as well as consumer surplus even without any costs, because of the premium pricing of branded products.