I suggest a way of extending Stalnaker’s account of assertion to allow for centered content. In formulating his account, Stalnaker takes the content of assertion to be uncentered propositions: entities that are evaluated for truth at a possible world. I argue that the content of assertion is sometimes centered: the content is evaluated for truth at something within a possible world. I consider Andy Egan’s proposal for extending Stalnaker’s account to allow for assertions with centered content. I argue that Egan’s account does not succeed. Instead, I propose an account on which the contents of assertion are identified with sets of multi-centered worlds. I argue that such a view not only provides a plausible account of how assertions can have centered content, but also preserves Stalnaker’s original insight that successful assertion involves the reduction of shared possibilities.