This paper considers the hypothesis that the coordination of cognitive operations in object counting depends on a limited-capacity central system, which may constrain children's counting performance. Different models of performance are considered in the light of knowledge about object counting. Four experiments varied the demands imposed by counting on any central coordinating system, by simultaneously manipulating the difficulty of visual and verbal components. Using children of different ages, all studies showed the effects of simultaneous manipulations of difficulty were additive, implying that the integration of visual and verbal information does not simultaneously draw on a common general purpose resource. It is suggested that while counting provides an example of a complex skill involving the coordination of processing in separate modules, a description of performance need not include a central executive as a limited capacity coordinating device.