In open, arid environments with limited shelter there may be strong selection on small prey species to develop behaviors that facilitate predator avoidance. Here, we predicted that rodents should avoid predator odor and open habitats to reduce their probability of encounter with potential predators, and tested our predictions using a native Australian desert rodent, the spinifex hopping-mouse (Notomys alexis). We tested the foraging and movement responses of N. alexis to non-native predator (fox and cat) odor, in sheltered and open macro- and microhabitats. Rodents did not respond to predator odor, perhaps reflecting the inconsistent selection pressure that is imposed on prey species in the desert environment due to the transience of predator-presence. However, they foraged primarily in the open and moved preferentially across open sand. The results suggest that N. alexis relies on escape rather than avoidance behavior when managing predation risk, with its bipedal movement probably allowing it to exploit open environments most effectively.