The optimal price of each firm falls in the search cost of consumers, in the limit to the monopoly price, despite the exit of lower-value consumers in response to costlier search. Exit means that fewer inframarginal consumers remain. The decrease in marginal buyers is smaller, because part of demand is composed of customers coming from rival firms. These buyers can be held up and are not marginal. Higher search cost reduces the fraction of incoming switchers among buyers, which decreases the hold-up motive, thus the price.