We define simple-regular expressions and languages. Simple-regular languages provide a necessary condition for a language to be outfix-free. We design algorithms that compute simple-regular languages from finite-state automata. Furthermore, we investigate the complexity blowup from a given finite-state automaton to its simple-regular language automaton and show that there is an exponential blowup. In addition, we present a finite-state automata construction for simple-regular expressions based on state expansion.