Definition of security under the framework of Environmental Security (a.k.a Network-Aware Security or Universally Composable Security) typically requires “extractability” of the private inputs of parties running a protocol. Formalizing concepts that appeared in an earlier work [19], we introduce a framework of “Monitored Functionalities,” which allows us to avoid such a requirement from the security definition, while still providing very strong composition properties. We also consider a specialization of the Environmental Security framework by designating one party as a “server” and all other parties as clients. Both these contributions in the work are aimed at being able to provide weaker Environmental Security guarantees to simpler protocols. We illustrate the usability of the Monitored Functionalities framework by providing much simpler protocols in the plain model than in [19] for some limited functionalities in the server-client model.