The allocation of free allowances for firms belonging to the carbon leakage list of the European Union Emissions Trading Scheme (EU ETS) was found to lead to substantial overcompensation, which is why some stakeholders recently have called for a phasing out of free allowances in the near term. This paper analyzes the consequences of phasing out free allowances in a dynamic two- period model when one group of countries unilaterally implements climate policies such as an emissions trading scheme. A carbon price induces firms to invest in abatement capital, but may also lead to the relocation of some firms. The social planner addresses the relocation problem by offering firms transfers, i.e. free allowances, conditional on maintaining the production in the regulating country. If transfers are unrestricted in both periods, then the social planner can implement the first best by setting the carbon price equal to the marginal environmental damage and using transfers to prevent any relocation. However, if transfers in the future period are restricted, it is optimal to implement a declining carbon price path with the first period price exceeding the marginal environmental damage. A high carbon price triggers investments in abatement capital and thus creates a lock-in effect. With a larger abatement capital stock, firms are less affected by carbon prices in the future and therefore less prone to relocate in the second period where transfers are restricted.