Consumers only discover at the first seller which product best fits their needs, then check its price online, then decide on buying. Switching sellers is costly. Equilibrium prices fall in the switching cost, eventually to the monopoly level, despite the exit of lower-value consumers when changing sellers becomes costlier. More expensive switching makes some buyers exit the market, leaving fewer inframarginal buyers to the sellers. Marginal buyers may change in either direction, so for a range of parameters, all firms cut prices.