Which and how many attributes are relevant for the sorting of agents in a matching market? This paper addresses these questions by constructing indices of mutual attractiveness that aggregate information about agents' attributes. The first k indices for agents on each side of the market provide the best approximation of the matching surplus by a k-dimensional model. The methodology is applied on a unique Dutch household survey containing information about education, height, BMI, health, attitude towards risk and personality traits of spouses. Three important empirical conclusions are drawn. First, sorting in the marriage market is not unidimensional: individuals face important trade-offs between the attributes of their spouses which are not amenable to a single-dimensional index. Second, although education explains a quarter of a couple's observable surplus, personality traits explain another 20%. Third, different personality traits matter differently for men and for women.