There is growing evidence that climate change and economic inequality are strongly interlinked. Furthermore, many climate policies have significant redistributive effects, and risk to widen inequalities. While carbon taxes are recognised to be an important tool for mitigating climate change in an efficient and effective way, it is also recognised that they should be accompanied by proper compensatory mechanisms, such as dividends, to avoid regressive effects. However, many analyses, including for Belgium, do not sufficiently consider long-term dynamics and the heterogeneous redistributive effects a carbon tax and dividend scheme can have on people living on low incomes. In this talk, I will present the results of an ex ante simulation of a carbon tax and dividend scheme in Belgium, targeted at reducing greenhouse gas emissions from heating and private transport by households. I argue that carbon tax and dividend schemes should be accompanied by other measures which help the poor to reduce their emissions, to ensure that these schemes do not become regressive, even when they are distributionally neutral or progressive in their original design.