When is it permissible to allow a newborn infant to die on the basis of their future quality of life? The prevailing official view is that treatment may be withdrawn only if the burdens in an infant's future life outweigh the benefits. In this paper I outline and defend an alternative view. On the Threshold View, treatment may be withdrawn from infants if their future well-being is below a threshold that is close to, but above the zero-point of well-being. I present four arguments in favor of the Threshold View, and identify and respond to several counter-arguments. I conclude that it is justifiable in some circumstances for parents and doctors to decide to allow an infant to die even though the infant's life would be worth living. The Threshold View provides a justification for treatment decisions that is more consistent, more robust, and potentially more practical than the standard view.