Consumers often make decisions about products using limited information. We develop an approach to measure and model the role of brand and price in facilitating these decisions through the formation of subjective product perceptions. This is accomplished by combining a pick-any-J data with a discrete choice experiment. We apply our approach to experimental data to learn the degree to which brand and price serve as signals about other attributes. We demonstrate the conditions and study design required to identify the parameters of brand and price separately from those of latent perceptions cued by brand and price. We demonstrate the value of our approach by constructing counterfactual experiments where we show how additional (perceptual) information can be strategically introduced to increase consumer preference and choice share. Taken collectively, our research contributes to the literature by empirically refining existing theory about how brand and price are interpreted by consumers. It also provides practical guidance for marketing tasks involving limited information environments, both digital and physical. Such environments include online search, retail packaging, website development, and most forms of advertising.