The literature on ordered search has assumed consumers to search optimally. In contrast, I investigate a price-competition model in which consumers are boundedly rational and firms use persuasive advertising to influence the consumers' aspiration price, i.e., the price regarded as 'satisfactory'. I consider various variants of the model capturing different consumers' second-best strategies if they do not find any satisfactory price. I derive a number of results including (i) predictions about the correlation between firm prominence and important market indicators, such as profits and conversion rates, that can help explain empirical evidence, (ii) extensions of the basic model, such as an analysis of the relationship between the consumer satisfaction rate and firms profits, and (iii) policy implications of the model.