Explanations for the attentional blink (AB; a deficit in identifying the second of two targets when presented 200-500ms after the first) have recently shifted from limitations in memory consolidation to disruptions in cognitive control. With a new model based on the threaded cognition theory of multi-tasking we propose a different explanation: the AB is produced by an overexertion of control. This overexertion is produced by a production rule that blocks target detection during memory consolidation. In addition to fitting many known effects in the literature, the model predicts that adding certain secondary tasks will decrease the AB. In Experiment 1, a secondary task is added to the AB task in which participants have to respond to a moving dot. As predicted, AB decreases. Experiment 2 expands this result by controlling for learning, and adds a second variation, rotating the first target. For this variation the model predicts an increase in AB, which is indeed what we found. (Contains 2 tables and 16 figures.)