The technical problem addressed in this paper is, given two rule systems for consequence relations X and Y, how to construct Y-approximations of a given X-relation. While an upper Y-approximation can be easily constructed if all Y-rules are Horn, the construction of lower Y-approximations is less straightforward. We address the problem by defining the notion of co-closure under co-Horn rules, that can be used to remedy violation of certain rules by removing arguments. In particular, we show how the co-closure under Monotonicity can be used to construct the monotonic restriction of a preferential relation. Unlike the more usual closure under the rules of M, this co-closure operator supports the intuition that preferential reasoning is more liberal than monotonic reasoning. The approach is embedded in a general framework for comparing rule systems for consequence relations. A salient feature of this framework is that it is also possible to compare rule systems that are not related by metalevel entailment.