Because interaction of the cerebral hemispheres has been found to aid task performance under demanding conditions, the present study examined how this effect is moderated by computational complexity, the degree of lateralization for a task, and individual differences in asymmetric hemispheric activation (AHA). Computational complexity was manipulated across tasks either by increasing the number of inputs to be processed or by increasing the number of steps to a decision. Comparison of within- and across-hemisphere trials indicated that the size of the between-hemisphere advantage increased as a function of task complexity, except for a highly lateralized rhyme decision task that can only be performed by the left hemisphere. Measures of individual differences in AHA revealed that when task demands and an individual's AHA both load on the same hemisphere, the ability to divide the processing between the hemispheres is limited. Thus, interhemispheric division of processing improves performance at higher levels of computational complexity only when the required operations can be divided between the hemispheres.