This is a pilot study to collect preliminary data for a larger, multicenter clinical trial proposal. The study will examine two strategies commonly used to treat preterm infants diagnosed with a patent ductus arteriosus (PDA). The PDA closes after birth for most term infants, but in many preterm infants, it remains open (patent). A PDA may present a complication for a number of short-term problems faced by preterm infants. Longer-term issues include the development of pulmonary hypertension and changes in the size and performance of the heart. There is ongoing debate as to whether or not the PDA requires intervention.