When consumers face a large number of alternatives, they tend to simplify the decision problem by reducing the number of available alternatives to a subset of relevant alternatives, i.e. a consideration set. Since consideration sets are typically unobserved, most studies in the demand literature have to assume a consideration model. If these consideration models are misspecified, the demand estimates can be biased. In this paper, we develop an approach to formally test any two competing models of consideration against one another in order to determine which model fits the data best. Our test follows the intuition of a menu approach and uses supplemental data on marginal cost-shifters to construct overidentifying restrictions. We show an application to German retailing of coffee and milk. We find that consideration sets are fundamentally different for coffee and milk, and relate our findings to differences in demand and supply conditions of the two product categories.