As in many areas of science, infant research suffers from low power. The problem is further compounded in infant research because of the difficulty in recruiting and testing large numbers of infant participants. Researchers have been searching for a solution and, as illustrated by this special section, have been focused on getting the most out of infant data. We illustrate one solution by showing how we can increase power in visual preference tasks by increasing the amount of data obtained from each infant. We discuss issues of power and present work examining how, under some circumstances, power is increased by increasing the precision of measurement. We report the results of a series of simulations based on a sample of visual preference task data collected from three infant labs showing how more powerful research designs can be achieved by including more trials per infant. Implications for infant procedures in general are discussed.