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In the abstraction refinement approach to model checking, the discovery of spurious counterexamples in the current abstract model triggers its refinement. The proof - produced by a SAT solver - that the abstract counterexamples cannot be concretized can be used to identify the circuit elements or predicates that should be added to the model. It is common, however, for the refinements thus computed to be highly redundant. A costly minimization phase is therefore often needed to prevent excessive growth of the abstract model. In This work we show how to modify the search strategy of a SAT solver so that it generates refinements that are close to minimal, thus greatly reducing the time required for their minimization.