This article examines the attentional limits responsible for task slowing in the overlapping task (refractory period) paradigm. Five experiments are reported in which stimulus factors were manipulated in visual search tasks performed in isolation or temporally overlapping with another task. Bottleneck models suggest that second-task slowing is caused by postponement of "attention-demanding" stages of the second task, while earlier "automatic" stages proceed unhindered. A prediction was derived from this class of models, namely that in the overlapping task condition the effect of second task factors that slow automatic stages should be reduced, whereas the effect of factors slowing later nonautomatic stages should be unchanged. The data (Experiments 1-4) exhibit such a pattern and suggest that encoding and comparison stages of the second task, but not response selection, occur in parallel with work on the first task. The absence of overadditive interactions in these experiments, and also the effects of manipulating first-task factors in Experiment 5, seems to argue against capacity sharing as the source of the slowing in this task combination. Some implications of these results for attention theory are discussed.