A carbon tax is effective at curbing carbon emissions, but it is met with low public support due to its high personal cost. Investigations have been conducted to reform carbon tax design to ease the burden on individuals by providing economic compensation, but the cost for governments is high. We propose a new cost-efficient solution by introducing people to a pre-existing reward-based climate policy to create a sense of economic compensation. Across three experiments, we show that the presence of a pre-existing reward-based climate policy increases participants' support for a carbon tax, especially when the innate connection between the two policies is made salient and people regard the reward as compensation for the tax. In contrast, if people are distracted from sensing this interrelationship, support for the tax does not differ from when it is introduced alone. Applicability of this approach was tested under different conditions where the pressure to reduce carbon emission is either high or low.