Successfully navigating a dynamic environment requires the efficient distribution of finite neural resources. Voluntary (endogenous) covert spatial attention selectively allocates those processing resources to goal-relevant locations in the visual scene in the absence of eye movements. However, the allocation of spatial attention is not always voluntary; abrupt onsets in the visual periphery automatically enhance processing of nearby stimuli (exogenous attention). In dynamic environments, exogenous events and internal goals likely compete to determine the distribution of attention, but how such competition is resolved is not well understood. To investigate how exogenous events interact with the concurrent allocation of voluntary attention, we used a speed-accuracy trade-off (SAT) procedure. SAT conjointly measures the rate of information accrual and asymptotic discriminability, allowing us to measure how attentional interactions unfold over time during stimulus processing. We found that both types of attention sped information accrual and improved discriminability. However, focusing endogenous attention at the target location reduced the effects of exogenous cues on the rate of information accrual and rendered negligible their effects on asymptotic discriminability. We verified the robustness of these findings in four additional experiments that targeted specific, critical response delays. In conclusion, the speed and quality of visual processing depend conjointly on internally and externally driven attentional states, but it is possible to voluntarily diminish distraction by irrelevant events in the periphery.