In this paper, a new model for the embodied exergy payback period is presented, which considers the exergy savings during acceleration and take-off, climb, trim-level cruise, descent and thrust reversal in landing for each flight versus higher exergy embodiment of composites that are used during manufacturing when compared to metals. The research work has ramifications for determining the optimum balance of lightweight and conventional material usage, thus improving the economic and environmental performance of aircraft for decoupling sustainable aviation and carbon dioxide emissions. The research work concludes with a vision for nearly-zero exergy aviation that involves a complete set of measures for the airside and landside. Considering new metrics for fuel savings and CO2 emissions based on exergy, the use of composite materials in new aircraft requires support from air traffic optimisation, jet fuel produced from renewable energy systems, nearly-zero exergy airport terminals, and sustainable taxiing solutions. The research work has the potential for supporting the carbon neutral growth strategy of the aviation sector.