Multiparty sessions with asynchronous communications and global types play an important role for the modelling of interaction protocols in distributed systems. In designing such calculi the aim is to enforce, by typing, good properties for all participants, maximising, at the same time, the behaviours accepted. The global types presented in this paper improve the state-of-the-art by extending the set of typeable asynchronous sessions and preserving decidability of type checking together with the key properties of Subject Reduction, Session Fidelity and Progress.