It has been proposed that grammars generally prefer to make the shortest possible move [Shortest], given the choice between two or more movers. It has also been proposed that there are general bans on movement which is in some sense too short [anti-locality]. What happens when the shortest move is too short? In this paper, I argue that elements which cannot move as a result of anti-locality are rendered irrele- vant for Shortest, and show that this provides a novel account of patterns of symmetry and asymmetry in Luganda and Haya passives. There we will see a curious pattern: internal arguments may move across no more than one other postverbal argument. The theory developed leads to a simple explanation of these effects. Movement of one ele- ment across another indicates that the crossed element is too close to the landing site to undergo movement; but given a particular definition of anti-locality, only one element may be anti-local to a given landing site.