Recently linear 0–1 programming methods have been successfully applied to the satisfiability problem of propositional logic. We present a preprocessing method that simplifies the linear 0–1 integer problem corresponding to a clausal satisfiability problem. Valid extended clauses, a generalization of classical clauses, are added to the problem as long as they dominate at least one extended clause of the problem. We describe how to efficiently obtain these valid extended clauses and apply the method to some combinatorial satisfiability problems. The reformulated 0–1 problems contain less but usually stronger 0–1 inequalities and are typically solved much faster than the original one with traditional 0–1 integer programming methods.