Competitiveness and carbon leakage issues have been some of the main concerns in the implementation and discussions of climate policies. These concerns are particularly important in the presence of multiple carbon markets since differences in climate change policy approaches may have impacts on the relative competitiveness of domestic sectors in countries with more stringent policies, and on the environmental effectiveness through carbon leakage. This paper examines the macroeconomic and sectoral competitiveness and carbon leakage impacts associated with a range of stylised mitigation policy scenarios. The scenarios reflect different depictions of carbon markets in terms of their level of linkages, their coverage (i.e. number of countries participating, types of gases and sectors) and the stringency of the carbon pricing policy across countries. The paper also investigates some policies to address competitiveness and carbon leakage issues. The analysis considers border carbon adjustments (BCAs) as well as direct and indirect (offset-based) linking of carbon markets. The results show that in presence of multiple carbon markets, competitiveness can decrease in countries that undertake climate policies, also leading to carbon leakage. The negative sectoral competitiveness and leakage effects can be reduced when more countries act, more emission sources are covered, and when the climate mitigation policy is harmonised across countries. The results also show that response policies, such as BCAs and linking of carbon markets, can address some, but not all, of the competitiveness and carbon leakage issues. While BCAs are more effective in addressing domestic competitiveness concerns than linking instruments, the latter are better in preserving the welfare of countries that are not undertaking a climate policy.