In this paper, we compare different mitigation policies when housing investments are irreversible. We use a general equilibrium model with non-homothetic preferences and an elaborate setup of the residential housing and energy production sector. In the first-best transition, the energy demand plays only a secondary role. However, this changes when optimal carbon taxes are not available. While providing subsidies for retrofits results in the lowest direct costs for households, it ultimately leads to the highest aggregate costs and proves to be an ineffective way to decarbonize the economy. In the second-best context, a phased-in carbon price outperforms the subsidy-based transition.