I erect a framework within the semantic view of theories for explaining the empirical success of internally inconsistent models and theories, with scientific realism in mind. The framework is an instance of the ‘content-driven’ approach to inconsistency, advocated by both Norton (Philos Sci 54:327–350, 1987) and Smith (Stud Hist Philos Sci 19:429–445, 1988a, In: Fine A, Leplin J (eds) PSA1988, 1988b), whose ideas my analysis aims to clarify and substantiate.