A major challenge in climate change negotiations lies in devising an effort-sharing method perceived as fair by most, if not all, governments. The United Nations Framework Convention on Climate Change emphasizes two core fairness principles for sharing mitigation efforts: common but differentiated responsibilities, which holds that nations with higher greenhouse gas emissions should contribute more, and respective capabilities, which asserts that economically advantaged countries should exert more efforts. These principles, while compelling, may conflict in practice. This paper introduces and axiomatically characterizes a family of effort-sharing methods designed to balance these principles. The proposed methods are computationally efficient and their practical relevance is demonstrated using global data.