An animal's ability to avoid predation likely depends on its ability to detect approaching predators, conceal itself, and seek refuge or protection from predators. Habitat, especially vegetation structure, can influence all of these factors concurrently. Binary categorical assessments of habitat as ‘open’ or ‘closed’, however, confound at least two functions of habitat structure that could influence the perceived risk of predation: concealment, which functions to hide an individual, and visibility, which enhances detection of a potential predator. Both can influence predation risk independently and simultaneously. In this study, we decoupled these functional properties of vegetation and studied the effects of concealment, visibility, and proximity to a refuge on the distance at which pygmy rabbits (Brachylagus idahoensis) fled from an approaching threat (flight initiation distance; FID). Concealment by vegetation decreased perceptions of risk; however, pygmy rabbits exhibited elevated risk at high levels of visibility, regardless of the amount of concealment. Proximity to burrow entrances also influenced perceptions of risk, such that risk was significantly lower when rabbits were on or near burrow systems. Disentangling the functional properties of habitat can provide a more comprehensive understanding of the factors that influence perceived risk and escape behaviors of prey and provide insight into how habitat structure mechanistically relates to predation risk.