We carry out a detailed sensitivity analysis of border carbon adjustment (rates) by applying a global Computable General Equilibrium (CGE) GTAP7-based model. We find different incentives for the regions in the climate coalition to raise carbon-based border tax rates (BTAX) above the standard rate that mimics an equalisation of carbon prices across regions. Herein, the strategic use of BTAX (the manipulation of the terms of trade) is stronger for all coalition regions than the environmental use (the reduction of carbon emissions abroad). Higher BTAX can reduce carbon leakage but with a declining marginal effect. Furthermore, we find different incentives for regions outside the coalition to oppose high BTAX rates: Russia and the other energy exporters would oppose it, while the Low-Income Countries would not because of benefits from the trade diversion effect. Thus, BTAX encourages the former to join the coalition, while compensating transfers are necessary to encourage the other (developing) countries including China and India.