Infants with hypoxic-ischaemic encephalopathy (birth asphyxia) have a high risk of death or disability. Those with poor prognosis are sometimes allowed to die after withdrawal of intensive care. In recent years, doctors have used new types of brain scan, magnetic resonance imaging (MRI), to predict the type and severity of impairment if the infant survives and to help with such decisions. In this thesis, I analyse the issues arising from the use of MRI for prognostication and decision-making in newborn infants. I argue that previous prognostic research has been hampered by a failure to identify and focus on the most important practical question and that this contributes to uncertainty in practice. I outline recommendations for improving research. I then look at existing guidelines about withdrawal of life-sustaining treatment. I identify several problems with these guidelines; they are vague and fail to provide practical guidance, they provide little or no genuine scope for parental involvement in decisions, and they give no weight to the interests of others. I argue that parental interests should be given some weight in decisions for newborn infants. I develop a new model of decision-making that, using the concept of a Restricted Life, attempts to set out clearly the boundaries of parental discretion in decision-making. I argue that where infants are predicted to have severe cognitive or very severe physical impairment parents should be permitted to request either withdrawal or continuation of treatment. I justify this model on the basis of overlapping interests, (prognostic, experiential and moral) uncertainty, asymmetrical harms, and the burden of care. In the conclusion, I set out a guideline for the use of MRI in newborn infants with hypoxic-ischaemic encephalopathy. I suggest that this guideline would provide a more robust, coherent and practical basis for decision-making in newborn intensive care.