We introduce a new bias for rule learning systems. The bias only allows a r
ule learner to create a rule that predicts class membership if each test of
the rule in isolation is predictive of that class. Although the primary mo
tivation for the bias is to improve the understandability of rules, we show
that it also improves the accuracy of learned models on a number of proble
ms. We also introduce a related preference bias that allows creating rules
that violate this restriction if they are statistically significantly bette
r than alternative rules without such violations.