Most commonly used inductive rule learning algorithms employ a hill-climbing search, whereas local pattern discovery algorithms employ exhaustive search. In this paper, we evaluate the spectrum of different search strategies to see whether separate-and-conquer rule learning algorithms are able to gain performance in terms of predictive accuracy or theory size by using more powerful search strategies like beam search or exhaustive search. Unlike previous results that demonstrated that rule learning algorithms suffer from over-searching, our work pays particular attention to the interaction between the search heuristic and the search strategy. Our results show that exhaustive search has primarily the effect of finding longer, but nevertheless more general rules than hill-climbing search. Thus, in cases where hillclimbing finds too specific rules, exhaustive search may help, while in others it may lead to over-generalization.