The attentional processes for tracking moving objects may be largely hemisphere-specific. Indeed, in our first two experiments the maximum object speed (speed limit) for tracking targets in one visual hemifield (left or right) was not significantly affected by a requirement to track additional targets in the other hemifield. When the additional targets instead occupied the same hemifield as the original targets, the speed limit was reduced. At slow target speeds, however, adding a second target to the same hemifield had little effect. At high target speeds, the cost of adding a same-hemifield second target was approximately as large as would occur if observers could only track one of the targets. This shows that performance with a fast-moving target is very sensitive to the amount of resource allocated. In a third experiment, we investigated whether the resources for tracking can be distributed unequally between two targets. The speed limit for a given target was higher if the second target was slow rather than fast, suggesting that more resource was allocated to the faster of the two targets. This finding was statistically significant only for targets presented in the same hemifield, consistent with the theory of independent resources in the two hemifields. Some limited evidence was also found for resource sharing across hemifields, suggesting that attentional tracking resources may not be entirely hemifield-specific. Together, these experiments indicate that the largely hemisphere-specific tracking resource can be differentially allocated to faster targets.