This paper presents an account of notional belief attributions, that is, belief attributions where the belief content is fully specified. The proposal combines a Hintikka style possible-worlds semantics for the belief operator and a structured meanings approach for giving a structured mode of presentation of the belief content. The semantics is not standard compositional, but it satisfies a more general notion of compositionality, explained in the paper. This notion, general compositionality, allows semantic switching: the semantic function relevant for an embedded term is distinct from that which applies to the term in which it is embedded. The general relation between compositionality and hyperintensional contexts is discussed in detail. In the first section, it is argued that we need to combine structured and unstructured meanings.