Unlike demand studies in other industries, models of provider demand in health care often omit a price (or any other factor) that equilibrates the market. Estimates of the consumer response to quality may consequently be attenuated, if the limited availability of individual providers prevents some consumers from seeing higher quality providers. We propose a tractable method to address this problem by adding a congestion effect to standard discrete-choice models. We show analytically how this improves forecasts of the market response to quality changes. We then apply this method to the market for heart surgery, and find that the attenuation bias in estimated quality effects can be important empirically. Consequently, existing assessments may understate the extent to which quality measures can improve patient outcomes, especially if such quality initiatives can be partnered with targeted expansions of provider capacity.