<p>Iconic memory for position is often characterized as “vast” or “limitless.” Yet typical studies of iconic memory have used only small stimulus sets and have restricted judgments to categorical visual content like letter identities or object features, the kinds of items that are known to be subject to very restrictive bottlenecks in recognition or working memory. To test whether iconic memory has greater capacity for purely spatial information, we measured the ability of observers to notice discrete illuminated positions in a yes/no partial report task. Contrary to the notion of limitless capacity, we found that observers could report only a fraction of the presented positions when the stimulus set contained dozens of items. These limitations were likely due to crowding, a fundamental constraint on the ability to report precise spatial information. Our results highlight that, at least in certain perceptual contexts, iconic memory for spatial position is far more limited than sometimes assumed.</p>