Abstract
This paper discusses some simple and natural restrictions of regulated pushdown automata, whose moves are regulated by some control languages. Most importantly, it studies one-turn regulated pushdown automata and proves that they characterize the family of recursively enumerable languages. In fact, this characterization holds even for atomic one-turn regulated pushdown automata of a reduced size. This result is established in terms of acceptance by final state and empty pushdown, acceptance by final state, and acceptance by empty pushdown.