The daily metabolizable energy intake of an animal is potentially limited by either the available feeding time or by its capacity to process energy. Animals are generally considered not to be time-limited but rather to be energy-processing-limited. This is concluded from the common observation that an animal's feeding time per day increases with a decrease in food density. We argue that such changes in feeding time are in theory also expected when no constraints are operating. Thus, a study of the constraints on energy intakes of free-living animals should be performed during demanding phases of the year. As an example, we collected data on time and energy budgets of Bewick's swan (Cygnus columbianus bewickii) refuelling during migration on fennel pondweed (Potamogeton pectinatus) tubers in two years differing two-fold in tuber biomass density. As predicted by time limitation, the feeding time (defined as the time with the head submerged) did not change in response to a change in food biomass density, both within and between years (averaging 12.2 h d−1). Contrary to energy-processing limitation, and again in line with time limitation, the daily metabolizable energy intake varied, being greater in the year with high than in the year with low food densities. We conclude that more studies are needed of animals operating under demanding conditions before it can be assessed whether free-living animals are generally energy-processing- or time-limited.