Late preterm and early term birth is associated with adverse short- and long-term consequences, particularly for neurodevelopment. A clear reduction in these births can be achieved by avoidance of non-medically indicated births prior to 39 weeks gestation, as shown following the introduction of prohibitive policies in the USA. However, clinicians and policy-makers must always consider the potential for unintended adverse consequences of such action, such as a potential for an increase in term stillbirth. Finding the balance between optimising long-term neurological outcomes and avoiding rare but devastating term stillbirths is one of the challenges of modern maternity care. In this article we review the current evidence for whether this balance can be found, where early births can be safely prevented, and what remains to be addressed to optimise this balance safely.