Recent trade models determine the equilibrium distribution of firm-level efficiency endogenously and show that freer trade shifts the distribution towards higher average productivity due to entry and exit of firms. These models ignore the possibility that freer trade also alters the firm-size distribution via international firm migration (offshoring); firms must, by assumption, produce in their 'birth nation.' We show that when firms are allowed to switch locations, new productivity effects arise. Freer trade induces the most efficient small-nation firms to move to the large nation. The big country gets an 'extra helping' of the most efficient firms while the small nation's firm-size distribution is truncated on both ends. This reinforces the big-nation productivity gain while reducing or even reversing the small-nation productivity gain. The small nation is nevertheless better off allowing firm migration.