Summary 1.?The shape of the function linking predator-attack success rate with distance to predator-concealing cover, or prey refuge, will affect population dynamics, distribution patterns and community trophic structure. Theory predicts that predator-attack success should decline exponentially with distance from predator-concealing cover, resulting in a threshold distance value above which there is little change in risk. Animals should then completely avoid areas of otherwise suitable habitat below this threshold, except when starvation risk exceeds predation risk. 2.?We measured the shape of the function linking attack success with distance from cover in a system of Eurasian Sparrowhawks Accipiter nisus attacking (n?=?445) and killing (n?=?71) Redshanks Tringa totanus. We then determined if there was a threshold value and whether redshanks avoided areas below this threshold. 3.?Sparrowhawk success rate with distance to predator-concealing cover declined exponentially with a threshold value of approximately 30?m. Redshanks used habitat above the threshold according to profitability and only fed below it, on average, in cold weather when starvation risk can be imminently high. Above about 5°C, 26% of available habitat was avoided. 4.?Our data support the hypothesis that predators create discrete areas with respect to cover that are avoided by prey. Large areas of suitable habitat may be unused, except in times of high starvation risk, when such areas may provide a foraging reserve, with large implications for population distribution and dynamics. 5.?Our results are generated from a system in which predators attack their prey from concealing cover. But in the theoretically identical reverse scenario where the prey animal?s distance from protective cover determines predation risk, such non-lethal effects will be equally important, especially in heavily fragmented landscapes.