In July 2016, the European Commission presented its proposal for a regulation to reduce greenhouse gases emissions in sectors not covered by the emissions trading system with regard to post-2020 binding targets. The proposal extends the burden-sharing framework designed in 2008. This new burden-sharing, called by the European Commission as the Effort Sharing Regulation, is based on a GDP per capita rule and aims to reflect the economic capacity of each European Member State on the basis of its relative wealth. However, several papers have pointed out that this way of allocating emissions can result in great cost-inefficiencies, as the allocations do not take Member State abatement costs into account. The proposal acknowledges this issue and proposes a range of flexibility instruments (i.e., more than 15 flexibility options) that intend to enhance cost-effectiveness. This paper evaluates the proposal and analyzes the economic impacts of each flexibility option with respect to fairness and cost-effectiveness using a computable general equilibrium model. The performed analysis demonstrates that flexibility mechanisms that allow "inter-Member state flexibility" constitute the most efficient options. Specifically, they reduce compliance costs and, simultaneously, increase fairness between low-income Member States and high-income Member States.