We analyse competition in settings where customers vary in how many price offers they compare; some are ‘captive’ to just one supplier. Allowing firms to discriminate between customer types (captive or not) is bad for consumers overall when firms are symmetric and consumers cannot affect how many offers they see, but may be good otherwise. The effects of entry by a new firm depend on its pattern – i.e. which consumer segments the entrant serves. Entry within a non-captive segment is bad for consumers, but entry is pro-consumer in the case of ‘independent reach’, for which we also examine merger effects. A different type of mixed strategy equilibrium appears in the case of ‘nested reach’, with different firms competing in high and low price ranges. To explore how market outcomes depend on the pattern of competition, we solve the general three-firm case.