The paper shows that under realistic conditions the Internet does not always increase price competition. We explore the effect of the Internet on consumers’ search behavior in a competitive setting, where consumers need to gather information on two types of product attributes: “digital attributes” (which can be communicated on the Web at very low cost) and “non-digital attributes” (for which physical inspection of the product is necessary). In our model, consumers choose between two brands. Consumers are only familiar with the non-digital attributes of one (their own) brand. We show that the impact of the Internet on competition will be radically different depending on the importance of the products’ non-digital attributes. As expected, when non-digital attributes are relatively unimportant, the Internet leads to intense price competition. In the case where non-digital attributes are more important however, we show that monopoly pricing can be sustained under some conditions. More surprisingly, we show that in such cases the use of the Internet can lead to higher prices by discouraging consumers from engaging in search.