Visual attention selectively enhances the neural response to a task-relevant item. But what happens when an item outside the primary focus of attention is also relevant to the task at hand? In a dual-task fMRI experiment, we studied the responses in retinotopically organized visual cortex in such a situation. Observers performed an attention-demanding task in the fovea while another, unmasked stimulus appeared in the visual periphery. With respect to this latter stimulus, observers attempted to perform either a less or a more attentionally demanding task. Both tasks increased the BOLD response to the peripheral stimulus. Behaviorally, however, only the less demanding task was performed well, whereas the demanding task was carried out near chance. What could explain the discrepancy between BOLD response and behavioral performance? A control experiment revealed that the report of the less demanding feature was severely disturbed by a mask. Moreover, the visual attributes queried by the demanding task had a significantly shorter iconic memory persistence. We conclude that, in the dual-task situation, the focus of attention initially remains with the foveal task, but subsequently shifts to the former location of the peripheral stimulus. Such a belated shift to a peripheral iconic memory (futile in one case, informative in the other) would reconcile the similar BOLD response with the disparate behavioral performance. In summary, our results show that an enhanced BOLD response is consistently associated with attentional modulation, but not with behavioral performance.