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Given a cap on carbon emissions, what is the optimal transition from coal to gas and renewable energy? To answer this question, we model the dependence of the energy sector on both (1) polluting exhaustible resources and (2) long-lived capital such as power plants. To minimise adjustment costs, optimal investments in expensive renewable energy start before phasing out fossil-fuel consumption, and may even start before investing in gas-fired plants. Investment in gas-fired plants can reduce the need for expensive renewable investment in the short term, but they eventually need to be decommissioned to make room to carbon-free power in the long term. Simulations of the European Commission's Energy Roadmap illustrate and quantify these results.