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The set covering problem (SCP) is a well-known computationally intractable problem. We suggest here a two-phase heuristic to solve it. The first phase reduces substantially the size of the given SCP by removing some variables; the second phase applies a simple Lagrangian heuristic applied to the reduced problem. Construction and improvement heuristics are embedded in the Lagrangian solution approach. The construction heuristic provides good covers by solving small SCPs. The improvement heuristic inserts these covers into larger ones from which better covers are extracted, again by solving different but also small SCPs. The novelty lies in the reduction of the problem size by an effective variable-fixing heuristic, which, in practice, eliminates up to 95% of the variables of the problem without sacrificing the solution quality. Extensive computational and comparative results are presented.