Recommender systems play an important role in supporting the achievement of the United Nations sustainable development goals (SDGs). In recommender systems, explanations can support different goals, such as increasing a user's trust in a recommendation, persuading a user to purchase specific items, or increasing the understanding of the reasons behind a recommendation. In this paper, we discuss the concept of "sustainability-aware persuasive explanations" which we regard as a major concept to support the achievement of the mentioned SDGs. Such explanations are orthogonal to most existing explanation approaches since they focus on a "less is more" principle, which per se is not included in existing e-commerce platforms. Based on a user study in three item domains, we analyze the potential impacts of sustainability-aware persuasive explanations. The study results are promising regarding user acceptance and the potential impacts of suchexplanations.