As computing systems of all types grow in power and complexity, it is common to want to simultaneously execute processes with different timeliness constraints. Many systems use CPU schedulers derived from time-share algorithms; because they are based on best-effort policies, these general-purpose systems provide little support for real-time constraints. This paper describes BeRate, a scheduler that integrates best-effort and soft real-time processing using a best-effort programming model in which soft real-time application parameters are inferred from runtime behavior. We show that with no a priori information about applications, BeRate outperforms Linux when scheduling workloads containing soft real-time applications.