Experiments have established that CTLs do not require continuous antigenic stimulation for expansion. Instead, responses develop by a process of programmed proliferation which involves approximately 7-10 antigen-independent cell divisions, the generation of effector cells and the differentiation into memory cells. The effect of this program on the infection dynamics and the advantages gained by the program have, however, not been explored yet. We investigate this with mathematical models. We find that more programmed divisions can make virus clearance more efficient because CTL division continues to occur independent from antigenic stimulation when virus load drops to low levels. This results in stronger effector activity at low virus loads, and in a higher chance of virus extinction. On the other hand, the more programmed divisions occur, the less efficient the response is at preventing high acute virus loads and thus acute symptoms. The reason is that the programmed divisions are independent from antigenic stimulation, and an increase in virus load does not speed up the rate of CTL expansion. We hypothesize that the 7-10 programmed divisions observed in vivo represent an optimal solution to this trade-off which maximizes the chances to clear, while preventing excessive acute pathology. If the CTLs fail to clear the virus, however, we find that the properties of the programmed proliferation model are very similar to those derived from models which assume continuous antigenic stimulation. We discuss these results in the context of data from murine virus infections and explore implications for virus dynamics in CD4 helper-deficient hosts.