We measured the patch use behaviour of Bewick's swans (Cygnus columbianus bewickii) feeding on below ground tubers of fennel pondweed (Potamogeton pectinatus). We compared the swans' attack rates, foraging costs and giving-up densities (GUDs) in natural and experimental food patches that differed in water depth. Unlike most studies that attribute habitat-specific differences in GUDs to predation risk, food quality or foraging substrate, we quantified the relative importance of energetic costs and accessibility. Accessibility is defined as the extent to which the animal's morphology restricts its harvest of all food items within a food patch. Patch use behaviours were measured at shallow (ca 0.4 m) and deep (ca 0.6 m) water depths on sandy sediments. In a laboratory foraging experiment, when harvesting food patches, the swan's attack rate (m3 s1) did not differ between depths. In deep water the energetic costs of surfacing, feeding and trampling were 1.13 to 1.21 times higher than in shallow water with a tendency to spend relatively more time trampling, the most expensive activity. Taking time allocation as measured in the field into account, foraging in deep water was 1.26 times as expensive as in shallow water. In the lake the GUD in shallow water was on average 12.9 g m2. If differences in energetic costs were the only factor determining differences in GUDs, then the deep water GUD should be 14.2 g m2. Instead, the mean GUD in deep water was 20.2 g m2, and therefore energetic costs explain just 18% of the difference in GUDs. At deep sites, 24% of tuber biomass was estimated to be out of reach, and we calculated a maximum accessible foraging depth of 0.86 m. This is close to the published 0.84 m based on body measurements. A laboratory experiment with food offered at a depth of 0.89 m confirmed that it was just out of reach. The agreement between calculated and observed maximum accessible foraging depths suggests that accessibility largely explains the remaining difference in GUDs with depth, and it confirms the existence of partial prey refuges in this system.