There are good reasons to think natural languages are compositional. But compound nominals (CNs) are largely productive constructions that have proven highly recalcitrant to compositional semantic analysis. I evaluate existing proposals to treat CNs compositionally and argue that they are unsuccessful. I then articulate an alternative proposal according to which CNs contain covert indexicals. Features of the context allow a variety of relations to be expressed using CNs, but this variety is not expressed in the lexicon or the semantic rules of the language. This proposal accounts for the diversity of contents CNs can be used to express while preserving compositionality. Finally, I defend this proposal against some recent anti-contextualist arguments.