Usually, key-establishment protocols are suggested in a security model. However, there exist several different security models in the literature defined by their respective security notions. In this paper, we study the relations between the security models of key establishment. For the chosen security models, we first show that some proven key-establishment protocols are not secure in the more restricted security models. We then suggest two compilers by which we can convert a key-establishment protocol that is secure in a specific security model into a key-establishment protocol that is still secure in a more restricted security model.