This paper uses a Ramsey model with two types of capital to analyze the optimal transition to clean capital when polluting investment is irreversible. The cost of climate mitigation decomposes as a technical cost of using clean instead of polluting capital and a transition cost from the irreversibility of pre-existing polluting capital. With a carbon price, the transition cost can be limited by underutilizing polluting capital, at the expense of a loss in the value of polluting assets (stranded assets) and a drop in income. In contrast, policy instruments that focus on redirecting investments-such as feebates or environmental standards-prevent underutilization of existing capital, avoid stranded assets, and reduce short-term losses; but they reduce emissions more slowly and increase the intertemporal cost of the transition. The paper investigates inter- and intra-generational distributional impacts and the political acceptability of climate change mitigation policy instruments.