We explore the problem of providing explanations for pairwise comparisons based on an underlying additive model. We follow a step-wise approach and provide explanations that take the form of a sequence of preference statements. Each statement should be as meaningful, relevant and cognitively simple as possible for the explanation to be accepted by an explainee. More specifically, we describe several schemes allowing to derive new knowledge, in the form of comparative statements, from previously accepted ones. These schemes exploit a number of well-understood properties of the additive model, and we ensure the correctness of the overall explanatory sequences. While these different schemes may correspond to alternative explanation strategies, we specifically advocate the use of the covering scheme because it meets some desirable properties for explanations. Imposing cognitively simple steps comes at the price of completeness. However, experimental results show that we are able to provide insightful explanations in many cases.