1. Habitat heterogeneity and predator behaviour can strongly affect predator–prey interactions but these factors are rarely considered simultaneously, especially when systems encompass multiple predators and prey. 2. In the Arctic, greater snow geese Anser caerulescens atlanticus L. nest in two structurally different habitats: wetlands that form intricate networks of water channels, and mesic tundra where such obstacles are absent. In this heterogeneous environment, goose eggs are exposed to two types of predators: the arctic fox Vulpes lagopus L. and a diversity of avian predators. We hypothesized that, contrary to birds, the hunting ability of foxes would be impaired by the structurally complex wetland habitat, resulting in a lower predation risk for goose eggs. 3. In addition, lemmings, the main prey of foxes, show strong population cycles. We thus further examined how their fluctuations influenced the interaction between habitat heterogeneity and fox predation on goose eggs. 4. An experimental approach with artificial nests suggested that foxes were faster than avian predators to find unattended goose nests in mesic tundra whereas the reverse was true in wetlands. Foxes spent 3·5 times more time between consecutive attacks on real goose nests in wetlands than in mesic tundra. Their attacks on goose nests were also half as successful in wetlands than in mesic tundra whereas no difference was found for avian predators. 5. Nesting success in wetlands (65%) was higher than in mesic tundra (56%) but the difference between habitats increased during lemming crashes (15%) compared to other phases of the cycle (5%). Nests located at the edge of wetland patches were also less successful than central ones, suggesting a gradient in accessibility of goose nests in wetlands for foxes. 6. Our study shows that the structural complexity of wetlands decreases predation risk from foxes but not avian predators in arctic-nesting birds. Our results also demonstrate that cyclic lemming populations indirectly alter the spatial distribution of productive nests due to a complex interaction between habitat structure, prey-switching and foraging success of foxes. [ABSTRACT FROM AUTHOR]