In many industries, firms give consumers the opportunity to add (at a price) optional goods and services to a baseline product. The aim of our paper is to provide a theoretical model of add-on pricing in competitive environments with two new distinctive features. First, we discuss the choice of offering the add-on, assuming that this entails a fixed cost. Second, we allow firms to have a varying degree of market power over the add-on, associated with the ability to capture the value that consumers obtain from such an additional good/service. Our model shows that the conventional wisdom, according to which offering the add-on should unambiguously lower the price of the baseline product, is not always supported. In asymmetric equilibria, in which only one firm offers the add-on, baseline prices are higher if the firm's market power over the add-on is limited. The predictions of the model are confirmed by a hedonic price model on a dataset of cruises offered worldwide.