We study a market in which several firms potentially each supply a number of “brands” of fundamentally the same product. Consumers differ in which products they consider, and firms compete using (multi-dimensional) mixed pricing strategies. We show when firms apply uniform pricing across their brands, and when they use segmented pricing so that one “discount” brand is always priced below another. We explore the case of symmetric brands in particular. We discuss the impact of introducing a new brand, of imposing a requirement to set uniform prices across a firm’s brands, and of mergers between firms.