Slicing is one of a number of techniques for reducing the state space of specifications during verification. Unlike techniques as e.g. data abstraction slicing is precise: the slice exactly reflects the property to be verified. This necessitates keeping large parts of the specification. In this paper we relax this requirement and instead compute slices overapproximating the behaviour of the specification. This can lead to substantially smaller slices. We consequently adapt the technique of abstraction refinement to slicing as to improve the slice once a false negative is detected. Slicing thus becomes an incremental method: it starts with a small, minimal part of the specification and successively adds further parts until either the property under interest holds on the slice or a real counterexample is found. We show correctness and termination of our technique.