The two dominant schemes for rule-learning, C4.5 and RIPPER, both operate in two stages. First they induce an initial rule set and then they refine it using a rather complex optimization stage that discards (C4.5) or adjusts (RIPPER) individual rules to make them work better together. In contrast, this paper shows how good rule sets can be learned one rule at a time, without any need for global optimization. We present an algorithm for inferring rules by repeatedly generating partial decision trees, thus combining the two major paradigms for rule generation—creating rules from decision trees and the separate-and-conquer rule-learning technique. The algorithm is straightforward and elegant: despite this, experiments on standard datasets show that it produces rule sets that are as accurate as and of similar size to those generated by C4.5, and more accurate than RIPPER’s. Moreover, it operates efficiently, and because it avoids postprocessing, does not suffer the extremely slow performance on pathological example sets for which the C4.5 method has been criticized.