In a two-firm model where each firm sells a high-quality and a low-quality version of a product, customers differ with respect to their brand preferences and their attitudes towards quality. We show that the standard result of quality-independent markups crucially depends on the assumption that the customers' valuation of quality is identical across firms. Once we relax this assumption, competition across qualities leads to second-degree price discrimination. We find that markups on low-quality products are higher if consuming a low-quality product involves a firm-specific disutility. Likewise, markups on high-quality products are higher if consuming a high-quality product creates a firm-specific surplus.