Advocates of occasional identity have two ways of interpreting putative cases of fission and fusion. One way—we call it the Creative view—takes fission to involve an object really dividing (or being replicated), thereby creating objects which would not otherwise have existed. The more ontologically parsimonious way takes fission to involve merely the ‘separation’ of objects that were identical before: strictly speaking, no object actually divides or is replicated, no new objects are created. In this paper we recommend the Creative approach (...) as the best way of dealing with certain problem cases involving teletransportation. Our considerations yield novel takes on psychological-continuity theories of personal identity and survival, and on the puzzle of Theseus' ship. (shrink)