We assess the distributional impact of introducing a carbon tax in a small open economy, using the case of Poland. We use a dynamic general equilibrium model with a search mechanism in the labour market, soft-linked to a microsimulation model based on household budget survey data. We evaluate the impact on various income groups and on inequality. We account for four key channels: the direct (energy) and indirect (other goods) price effects, behavioural adjustment of consumption, and changes in labour income. We consider three of ways to recycle the carbon tax revenue: lump-sum transfer, energy price subsidies, and labour tax reduction. We find that the distributional effects depend on the recycling of revenues. Using them to reduce labor taxation attenuates the negative effect of carbon tax on GDP and employment but increases inequality compared to a lump-sum transfer to households. This finding highlights the trade-off between efficiency and equity. Our results could be relevant for other countries producing fossil fuels, such as South Africa, Germany, or Australia.