It is usually acknowledged that firms benefit from a large customer base in markets with switching costs. However, Klemperer [1995] argues that this may not be true if an increase in the size of a firm's customer base induces fierce price competition, making the firm worse off. This paper shows that such an outcome can be obtained under standard assumptions, such as homogeneous goods and uniformly distributed switching costs. In the model, firms have very limited incentives to fight for market shares, and the notion that switching costs make markets less competitive is stronger than previously shown.