This paper studies the optimal transition from existing coal power plants to gas and renewable power under a carbon budget. It solves a model of polluting, exhaustible resources with capacity constraints and adjustment costs (to build coal, gas, and renewable power plants). It finds that optimal investment in renewable energy may start before coal power has been phased out and even before investment in gas has started, because doing so allows for smoothing investment over time and reduces adjustment costs. Gas plants may be used to reduce short-term investment in renewable power and associated costs, but must eventually be phased out to allow room for carbon-free power. One risk for myopic agents comparing gas and renewable investment is thus to overestimate the lifetime of gas plants -- e.g., when computing the levelized cost of electricity -- and be biased against renewable power. These analytical results are quantified with numerical simulations of the European Commission's 2050 energy roadmap.