When observers try to identify successive targets in a visual stream at a rate of 100 ms per item, accuracy for the 2nd target is impaired for intertarget lags of 100-500 ms. Yet, when the same stream is presented more rapidly (e.g., 50 ms per item), this pattern reverses and a 1st-target deficit is obtained. M. C. Potter, A. Staub, and D. H. O'Connor (2002) accounted for these findings with a 2-stage competition theory (detection followed by identification) in which each stage is limited by its own pool of resources. In 5 experiments we varied the items that preceded the 1st target. The results show strong influences of these leading items on the 1st-target deficit, with almost no influence on 2nd-target accuracy. This is interpreted as strong support for multiple factors influencing target accuracy in rapid visual streams (J. Kawahara, J. T. Enns, & V. Di Lollo, 2006). (Contains 1 footnote and 6 figures.)