Abstract. Recently, notions of equivalence for Answer Set Programming have been studied intensively and were shown to be beneficial for modular programming and automated optimization. In [9], the novel notion of strong equivalence for logic programs with rule preferences (so-called ordered logic programs) has been defined and necessary and sufficient conditions for programs being strongly equivalent have been presented. In this paper, we extend this work and analyze a weaker notion of equivalence for ordered logic programs. Whereas strong equivalence makes great demands on ordered logic programs, the weakened notion enables program transformations for simplifying preference relations.