We propose a new unambiguous grammar formalism, referred to as ordered context-free grammars, which is identical to context-free grammars, apart from the property that it also places an order on parse trees. Since only a minor modification to ordered context-free grammars is required to obtain parsing expression grammars, the relationship between context-free grammars and parsing expression grammars becomes more evident. By preserving how ordered context-free grammars support left-recursion, parsing expression grammars is modified to support left recursion in ways much more natural than current approaches.