The concept of carbon budgets has become a key and effective tool in terms of communicating the existing environmental challenge and monitoring environmental policy, in the context of the Paris agreement. In this sense, the literature has addressed different mechanisms to distribute them by countries/groups according to reasonable distribution principles, among which fairness and efficiency play an essential role. Given the problem of agreeing on indicators by countries, the paper proposes the use of claims models as a basis for this distribution, which avoid using indicators and only have to agree on elements defining the distribution rules. In this sense and based on a reference of the available global Carbon Budget (Mercator) for 2018-2050, and the CO2 forecasts taken from the intermediate scenario SSP2-45 (Middle of the road) considered by the IPCC (2021), different distribution rules are addressed proposed by the literature (equality, proportional, and α-min) and are evaluated for the available groups of countries. Two relevant exercises are proposed beyond the initial distribution based on the previous theoretical rules: first, evaluate the cost of these distributions in terms of the welfare of each group (in particular, in terms of GDP); and two, use the GDP costs themselves to propose new distribution rules that are cost-efficient. The results imply having not only a global cost-efficient distribution proposal but also an annual path. We understand that the work is useful not only in terms of its methodological proposal but also as an alternative guide that structures future distribution policies. Keywords: allocation methods; claims; carbon budgets; climate change mitigation; equity JEL classification: D7; H4; H8; Q58; Q54