Climate policy exemptions for energy‐intensive sectors are often justified with distributional concerns. One concern is that households employed in energy‐intensive sectors might be affected disproportionally because of (international) capital mobility. By assuming that workers cannot move freely between sectors, we can reproduce this concern: uniform climate policy causes more inequality between the sectors when capital is mobile than when it is not. However, we find that affected households can be relieved more effectively with sector‐specific labour taxes than with sector‐specific climate policy. The reason for this finding is that households benefit more directly from sector‐specific labour tax cuts than from climate policy exemptions. Keeping climate policy uniform across sectors has the added benefit of creating incentives for long‐term decarbonisation. In addition, we find that the differential effect of capital mobility depends on the government's degree of inequality aversion – redistribution is more expensive when capital is mobile.