We construct a marriage market model of matching along multiple dimensions, some of which are unobservable, in which individual preferences can be summarized by a one-dimensional index combining the various characteristics. We show that, under testable assumptions, these indices are ordinally identified and that the male and female trade-offs between their partners’ characteristics are overidentified. Using PSID data on married couples, we recover the marginal rates of substitution between body mass index (BMI) and wages or education: men may compensate 1.3 additional units of BMI with a 1 percent increase in wages, whereas women may compensate two BMI units with 1 year of education.