Over 3,500 babies in New Zealand are born late preterm (4-6 weeks early) every year. Late preterm babies are at greater risk of disability when they get older than babies born at term. This may be because late preterm babies frequently have drops in the amount of oxygen in their blood for the first few weeks after birth. Caffeine is an effective treatment for these drops in oxygen saturation in babies born very preterm (more than eight weeks early) and reduces the risk of disability in very preterm babies. We are planning a trial to determine if caffeine will reduce disability in babies born late preterm. Before starting this trial, we need to determine the most effective dose of caffeine to use in late preterm babies. This study will help us select the best dose of caffeine to reduce the frequency of drops in oxygen saturation in late preterm babies.