Limits on the storage capacity of working memory significantly affect cognitive abilities in a wide range of domains, but the nature of these capacity limits has been elusive. Some researchers have proposed that working memory stores a limited set of discrete, fixed-resolution representations, whereas others have proposed that working memory consists of a pool of resources that can be allocated flexibly to provide either a small number of high-resolution representations or a large number of low-resolution representations. Here we resolve this controversy by providing independent measures of capacity and resolution. We show that, when presented with more than a few simple objects, human observers store a high-resolution representation of a subset of the objects and retain no information about the others. Memory resolution varied over a narrow range that cannot be explained in terms of a general resource pool but can be well explained by a small set of discrete, fixed-resolution representations.