Whenever we open our eyes, we are confronted with an overwhelming amount of visual information. Covert attention allows us to select visual information at a cued location, without eye movements, and to grant such information priority in processing. Covert attention can be voluntarily allocated, to a given location according to goals, or involuntarily allocated, in a reflexive manner, to a cue that appears suddenly in the visual field. Covert attention improves discriminability in a wide variety of visual tasks. An important unresolved issue is whether covert attention can also speed the rate at which information is processed. To address this issue, it is necessary to obtain conjoint measures of the effects of covert attention on discriminability and rate of information processing. We used the response-signal speed-accuracy tradeoff (SAT) procedure to derive measures of how cueing a target location affects speed and accuracy in a visual search task. Here, we show that covert attention not only improves discriminability but also accelerates the rate of information processing.