The term Presupposition Accommodation is standardly used to describe the situation when a presupposition that is not satisfied by the context doesn’t lead to an infelicitous utterance but rather makes the hearer pretend as if it was satisfied, in the spirit of Lewis (1979). Although the conditions under which this process can apply are still not well understood, it has been observed that there seems to be some correlation with the type of presupposition trigger and the difficulty to accommodate its respective presupposition, particularly with respect to those triggers which have been argued to be anaphoric like too and again (e.g. Kripke 1990/2009). In this on-going project, I am trying to develop a theory of accommodation and relate differences in accommodation difficulty to the respective underlying processes a discourse processor has to engage in. A starting hypothesis is that some accommodation processes might require the costly introduction of a discourse referent into the discourse model while others leave the discourse model untouched but merely require the assumption of the interlocutor’s reliability.