Foraging desert ants, Cataglyphis fortis, monitor their position relative to the nest by path integration. They continually update the direction and distance to the nest by employing a celestial compass and an odometer. In the present account we addressed the question of how the precision of the ant's estimate of its homing distance depends on the distance travelled. We trained ants to forage at different distances in linear channels comprising a nest entrance and a feeder. For testing we caught ants at the feeder and released them in a parallel channel. The results show that ants tend to underestimate their distances travelled. This underestimation is the more pronounced, the larger the foraging distance gets. The quantitative relationship between training distance and the ant's estimate of this distance can be described by a logarithmic and an exponential model. The ant's odometric undershooting could be adaptive during natural foraging trips insofar as it leads the homing ant to concentrate the major part of its nest-search behaviour on the base of its individual foraging sector, i.e. on its familiar landmark corridor.