The resolution of temporal attention is limited in a manner that makes it difficult to identify two targets in short succession. This limitation produces the phenomenon known as the attentional blink (AB), in which processing of a first target (T1) impairs identification of a second target (T2). In the AB literature, there is broad agreement that increasing the time it takes to process T1 leads to a larger AB. One might, therefore, predict that increasing the number of possible T1 identities, or target set, from 1 to 16 would lead to a larger AB. We were surprised to find that this manipulation of T1 difficulty had no influence on AB magnitude. In subsequent experiments, we found that AB magnitude interacts with T1 processing time only under certain circumstances. Specifically, when the T1 task was either well masked or had to be completed online, we found a reliable interaction between AB magnitude and the target set size. When neither of these conditions was fulfilled, there was no interaction between target set size and the AB. Previous research found that when the target set changes from trial to trial, trials with more possible targets elicited a larger AB. In the present study, the target set is held constant, reducing the demands on working memory. Nevertheless, AB magnitude still interacts with target set size, as long as the T1 task cannot be processed offline. Thus, the act of searching memory delays subsequent processing, even when the role of working memory has been minimized.