A weak double-dividend is the proposition that the welfare improvement from a green tax reform, where the revenue from an environmental tax is used to reduce other tax rates, must be greater than the welfare improvement from a reform where the environmental taxes are returned in a lump sum fashion. We show in this note that a weak double-dividend need not hold in a world with multiple distortions. In an economy with multiple distortions one must choose carefully which tax rates to reduce, or one can do worse than a lump sum redistribution of the environmental tax revenues.