Despite their importance for understanding predator–prey interactions, factors that affect predator evasion behaviours of offspring of large ungulates are poorly understood. Our objective was to characterize the influence of selection and availability of escape cover and maternal presence on predator evasion by white-tailed deer, Odocoileus virginianus, fawns in the northern Great Plains, U.S.A. We observed 45 coyote, Canis latrans, chases of fawns, and we participated in 83 human chases of fawns during 2007–2009, of which, 19 and 42 chases, respectively, ended with capture of the fawn. Evasive techniques used by fawns were similar for human and coyote chases. Likelihood of a white-tailed deer fawn escaping capture, however, was influenced by deer group size and a number of antipredator behaviours, including aggressive defence by females, initial habitat and selection of escape cover, all of which were modified by the presence of parturient females. At the initiation of a chase, fawns in grasslands were more likely to escape, whereas fawns in forested cover, cultivated land or wheat were more likely to be captured by a coyote or human. Fawns fleeing to wetlands and grasslands also were less likely to be captured compared with those choosing forested cover, wheat and cultivated land. Increased probability of capture was associated with greater distance to wetland and grassland habitats and decreased distance to wheat. Use of wetland habitat as a successful antipredator strategy highlights the need for a greater understanding of the importance of habitat complexity in predator avoidance.