Theoretical work on bounded rationality typically assumes a rich dataset of choices from many overlapping menus, limiting its practical applicability. In contrast, we study the problem of identifying the distribution of cognitive characteristics in a population of agents from a minimal dataset consisting of aggregate choice shares from a single menu (without adding observable covariates). Under homogeneous preferences, we show that both “consideration capacity” and “consideration probability” distributions can be recovered effectively when the menu is sufficiently large. This remains generically true when tastes are heterogeneous but their distribution is known. When the preference distribution is unknown, we demonstrate that joint choice share data from as few as three “occasions” are generically sufficient for full identification of the cognitive capacity distribution and provide sub- stantial information about tastes.