Concern that unilateral greenhouse gas emission reductions could foster carbon leakage and undermine the international competitiveness of domestic industry has led to growing calls for carbon-based border-tax adjustments (BTAs). This paper uses a global general equilibrium model to assess the economic effects of BTAs and comes to three main conclusions. First, BTAs can reduce carbon leakage if the coalition of countries taking action to reduce emissions is small, because in this case leakage (while typically small) mainly occurs through international trade competitiveness losses rather than through declines in world fossil fuel prices that trigger rising carbon intensities outside the region taking action. Second, the welfare impacts of BTAs are small, and typically slightly negative at the world level. Third, and perhaps more strikingly, BTAs do not necessarily curb the output losses incurred by the domestic energy intensive-industries (EIIs) they are intended to protect in the first place. This is in part because taken as a whole, EIIs in industrialised countries make important use of carbon-intensive intermediate inputs produced by EIIs in other geographical areas. Another, deeper explanation is that EIIs are ultimately more adversely affected by carbon pricing itself, and the associated contraction in market size, than by any international competitiveness losses. These findings are shown to be robust to key model parameters, country coverage and design features of BTAs.