Using the Chakravorty et al. (2006) ceiling model, we characterize the optimal consumption paths of three energy resources: dirty oil, which is non-renewable and carbon emitting; clean oil, which is also non-renewable but carbon-free thanks to an abatement technology, and solar energy, which is renewable and carbon-free. The resulting energy-mix can supply the energy needs of two sectors. These sectors differ in the additional abatement cost they have to pay for consuming clean rather than dirty oil, as Sector 1 (industry) can abate its emissions at a lower cost than Sector 2 (transport). We show that it is optimal to begin by fully capturing Sector 1's emissions before the ceiling is reached. Also, there may be optimal paths along which the capture devices of both sectors must be activated. In this case, Sector's 1 emissions are fully abated first, before Sector 2 abates partially. Finally, we discuss the way heterogeneity of abatement costs causes sectoral energy price paths to differ.