The main question examined in the present work was whether spatial attention can be deployed to an appropriate structural framework not only endogenously when the framework is displayed continuously, as in previous work, but also exogenously, when it is displayed transiently 100 ms before the target. The results of five experiments answered that question in the negative. We found that the onset transient triggered by a brief presentation of the structural framework did enhance the response to the upcoming target. That enhancement, however, was due not to the framework itself but to the alerting effect produced by its sudden onset, witness the finding that the same enhancement was produced by an onset transient triggered by a featureless stimulus (i.e., by a brief dimming of the entire screen, in the absence of a structural framework). We conclude that spatial attention can be deployed to the region demarcated by a structural framework when it is deployed endogenously but not when it is deployed exogenously. A theoretical account of the results is proposed in terms of the temporal dynamics of the locus cœruleus/norepinephrine neuromodulatory system.