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Assuming that the acquisition and retention Of memories have Costs, properties of memories should fit the functional requirements for the system Of memory Based on a functional analysis of what path integration is meant to (to, we predicted that odometric memories in desert. ants should show (I) little improvement with repeated training: performance should be as good after one training trial as after six training trials, (2) decay of memory after 24 h, and (3) performance based solely on the most. recent outbound trip, with no integration over multiple memories. Desert ants (Cataglyphis fortis) traveled in narrow straight. plastic channels to forage for cookie crumbs in a feeder at 6- or 12-m distance. Each ant was tested once by being taken front the feeder and released 2 in from the end of a 32-m channel to run home. The distance at which the ant first turned back (first turn) constituted the data. In acquisition, groups trained one or six times before being tested had unsystematic scatter that did not. differ significantly. In retention, ants tested after a 24-h delay showed larger unsystematic scatter than control animals tested after no delay. In integration, ants were trained five times at 6 or 12 m and then tested at, 12 or 6 in, respectively. No evidence of integration of multiple odometric memories was found. The results show that the properties of odometric memories. are indeed tailored to what the memory system is used for.