In this article we define various aspects, or parameters, of interactive narrative systems and present them as a framework that can help authors, creators and designers to conceive, analyze, or prioritize the narrative goals of a given sys- tem. We start by defining the Author-Audience distance (AAD), which in turn can be seen as a function of Narrative Intelligibility. AAD can also be influenced by the intended or unintended level of abstractedness or didascalicity (i.e. figurative- ness) of a given narrative. We define narrative intelligibility in complementarity with the related notion of Narrative Closure. We also make a distinction between the goals of the system and the goals of the narrative that it mediates, and consider the proposed parameters at two interrelated levels of analysis: the system level and the embedded narrative level, as the normative values and goals of these two le- vels should not be taken for granted.