Article dans une revue: This paper re-examines the spaceship problem, i.e. the design of the optimal population under a fixed living space, by focusing on the dilemma between adding new beings and extending the life of existing beings. For that purpose, we characterize, under time-additive individual welfare depending negatively on population density, the preference ordering of a utilitarian social planner over lifetime-equal histories, i.e. histories with demographic conditions yielding an equal finite number of life-periods (imposed by resources constraints). The analysis of the spaceship problem contradicts widespread beliefs about the populationism of Classical Utilitarianism and the antipopulationism of Average Utilitarianism. We also study the invariance property exhibited by various utilitarian rankings to the total space available and to individual preferences. Finally, we compare histories for a spaceship with a stationary population, and try to accomodate intuitions about posterity and renewal of populations.