To limit the loss of competitiveness when domestic firms are subject to stronger regulation than international competitors, a cap-and-trade policy can be associated either with partial grandfathering or with border adjustment. We compare the two policies from a domestic social-welfare point of view when distributional concerns matter. We exhibit the conditions under which these policies have to be implemented, and we show that exportside border adjustment welfare-dominates partial grandfathering. However, the former policy results in a higher profit in the export sector but both a lower consumer surplus and lower profits of domestic-market-oriented firms.