Assumption-based argumentation (ABA) is an argumentative formalism that allows for reasoning on the basis of defeasible assumptions and strict rules. Standard semantics for this formalism sometimes give rise to problematic behaviour in the presence of rules with assumptions in their heads. In this paper, we introduce a six-valued labelling semantics that overcomes these shortcomings while preserving all the usual properties of the standard Dung-style three-valued semantics for ABA frameworks, including existence of the complete semantics, uniqueness of the grounded semantics and preservation of the computational complexity of all main reasoning processes.