We investigate the recently proposed notion of serialisability of semantics for abstract argumentation frameworks. This notion describes semantics where the construction of extensions can be serialised through iterative addition of minimal non-empty admissible sets. We investigate general relationships between serialisability and other principles from the literature. We also investigate the novel unchallenged semantics as a new instance of a serialisable semantics and, in particular, analyse it in terms of satisfied principles and computational complexity.