In reality matching is not purely random nor perfectly assortative. We propose a parsimonious way to model the choice of whom to meet that endogenizes the degree of randomness in matching, and show that this allows for better identification of preferences. The model features an interaction between a productive and a strategic motive. For some preference specifications, there is a tension between these two motives that drives an endogenous wedge between the shape of sorting patterns and the shape of the underlying match payoff function, allowing for better empirical identification. We show the empirical relevance of our theoretical results by applying it to the U.S. marriage market.