The consequences of maintaining a task set in the context of the (speeded) attentional blink were investigated in a series of experiments. Observers were asked to either attend or ignore the first of two target stimuli (T1 and T2). The results showed that when T1 and T2 shared a task relevant feature that was unique to T2, but not to T1, a shallow attentional blink was observed, as well as a lack of Lag 1 sparing. In comparison, when the targets shared a feature that was uniquely task relevant to both targets, the blink could not be avoided. Conversely, when no feature was shared between targets, ignoring T1 was successful and virtually no attentional costs were apparent. A similar lack of costs was also observed when targets shared a task relevant feature that was unique to T1 but not to T2. Finally, matching the feature dimension of a target feature that was unique to T2, but not T1, also strongly attenuated the blink. However, it did not completely abolish Lag 1 sparing. The results are interpreted in the context of current models of the attentional blink.