In most data mining applications where induction is used as the primary tool for knowledge extraction from real world databases, it is difficult to precisely identify a complete set of relevant attributes. The paper introduces a novel rule induction algorithm called Rule Induction Two In One (RITIO), which eliminates attributes in the order of decreasing irrelevancy. Like ID3-like decision tree construction algorithms, RITIO makes use of the entropy measure as a means of constraining the hypothesis search space; but, unlike IDS-like algorithms, the hypotheses language is the rule structure and RITIO generates rules without constructing decision trees. The final concept description produced by RITIO is shown to be largely based on only the most relevant attributes. Experimental results confirm that, even on noisy, industrial databases, RITIO achieves high levels of predictive accuracy.