Abstract. Counterexample-guided abstraction refinement (CEGAR) is a key technique for the verification of computer programs. Grumberg et al. developed a CEGAR-based algorithm for the modal µ-calculus. There, every abstract state is split in a refinement step. In this paper, the work of Grumberg et al. is generalized by presenting a new CEGAR-based algorithm for the µ-calculus. It is based on a more expressive abstract model and applies refinement only locally (at a single abstract state), i.e., the lazy abstraction technique for safety properties is adapted to the µ-calculus. Furthermore, it separates refinement determination from the (3-valued based) model checking. Three different heuristics for refinement determination are presented and illustrated.