Life-sustaining treatment is sometimes withdrawn or withheld from critically ill newborn infants with poor prognosis. Guidelines relating to such decisions place emphasis on the best interests of the infant. However, in practice, parental views and parental interests are often taken into consideration. In this paper I draw on the example of newborn infants with severe muscle weakness (for example spinal muscular atrophy). I provide two arguments that parental interests should be given some weight in decisions about treatment, and that they should be given somewhat more weight in decisions about newborns than for older children. Firstly, the interests of the infant and of parents intersect, and are hard to separate. Parents' views about treatment may be relevant to an assessment of the infant's interests, and they may also affect those interests. Secondly, the interests of the infant in her future are relatively reduced by her developmental immaturity. In some situations parents' welfare interests outweigh those of the infant. However, I argue that this would not justify treatment limitation except in the setting of severe impairment.