On the journey to wintering sites, most migratory birds alternate between flights and stopovers, where they rest and refuel. In contrast to the time-minimization strategy commonly assumed to drive the pre-breeding migration, birds are rather expected to follow an energy minimization during post-breeding migration. It is the cumulative duration of flights and stopovers that determines the total energy requirements and duration of the journey. Since migrating birds actually spend most of the time at stopovers sites, selection to minimize the amount of energy or time spent on migration is likely to operate on the effectiveness of stopover rest and refueling. Here, we address the relative contribution of factors acting on departure decisions from a stopover site during the post-breeding migration in a long-distance migratory songbird. When capture probability is low, it is impossible to measure fattening over the entire duration of the stopover. To get around this limitation, we use time since arrival (TSA) as a proxy for the progressive temporal change occurring in the internal state of an individual (i.e. rest, physiological recovery, and fuel loading) during the stopover. We develop a capture–recapture model to address the respective effects of estimated TSA and of weather conditions on departure probability. Using a 20-year dataset for Sedge Warblers (Acrocephalus schoenobaenus), we show that TSA served as a surrogate of the most important information that birds use when deciding to depart from a stopover site, while low humidity and rising atmospheric pressure only slightly increase daily departure probability. Hence, a bird would resume migration mainly according to the time it had to rest and refuel, and then fine-tuning departure decision according to weather conditions. The generality of these results needs to be assessed by applying this modeling framework to other migratory species and at sites or times with greater weather variability.