Attribute reduction is an important issue of data mining. It is generally regarded as a preprocessing phase that alleviates the curse of dimensionality, though it also leads to classificatory analysis of decision tables. In this paper, we propose an efficient algorithm TWI-SQUEEZE that can find a minimal (or irreducible) attribute subset, which preserves classificatory consistency after two scans of a decision table. Its worst-case computational complexity is analyzed. The outputs of the algorithm are two different kinds of classifiers. One is an IF-THEN rule system. The other is a decision tree.