In this paper we consider a synchronous message passing system in which in every round an external adversary is able to send each processor up to k messages with falsified sender identities and arbitrary content. It is formally shown that this impersonation model is slightly stronger than the asynchronous message passing model with crash failures. In particular, we prove that (k+1)-set agreement can be solved in this model, while k-set agreement is impossible, for any k>=1. The different strength of the asynchronous and impersonation models is exhibited by the order preserving renaming problem, for which an algorithm with n+k target namespace exists in the impersonation model, while an exponentially larger namespace is required in case of asynchrony.