The fourth layer of narrative in Interactive Narrative Systems (INS), such as games, is the players’ re-tellings of the stories they have experienced when playing. The occurrence of re-tellings can be considered as an indicator for a well designed INS and as an instrument of critique - the experiences of play are important and memorable to such a degree to the players that they find them worthy to tell others about. The notion of the fourth layer is added to the structural model of IN Systems having (1) a base architectural layer giving conditions for a (2) second layer of narrative design, while a (3) third layer is the narrative discourse - eg. the unique, session-specific played or traversed sequences of events. In relation to this, the Story Construction model is described.