Numerous languages permit an NP that is not selected by the verb to be added to a clause, with several different possible interpretations. We divide such nonselected arguments into possessor, benefactive, attitude holder, and affected experiencer categories, on the basis of syntactic and semantic differences between them. We propose a formal analysis of the affected experiencer construction. In our account, a syntactic head Aff(ect) introduces the experiencer argument, and adds a conventional implicature to the effect that any event of the type denoted by its syntactic sister is the source of the experiencer's psychological experience. Hence, our proposal involves two tiers of meaning: the at-issue meaning of the sentence, and some not-atissue meaning (an implicature). A syntactic head can introduce material on both tiers. Additionally, we allow two parameters of variation: (i) the height of the attachment of Aff, and (ii) how much of the semantics is at-issue and how much is an implicature. We show that these two parameters account for the attested variation across our sample of languages, as well as the significant commonalities among them. Our analysis also accounts for significant differences between affected experiencers and the other types of non-selected arguments, and we also note a generalization to the effect that purely not-at-issue non-selected arguments can only be weak or clitic pronouns.