Avoiding potentially catastrophic global climate change is a moral imperative, demanding significant reductions in greenhouse gas emissions from all important transport sectors, including aviation. However, because passenger flights and freight traffic are increasing much faster than efficiency improvements, the aviation sector will not be able to reduce emissions, or even stabilize them at current levels, without direct, forceful action to reduce demand. This paper reviews the ethical principles and empirical realities supporting the case for reducing worldwide aviation traffic. It argues that most passenger air travel and air freight shipping represents unnecessary luxury consumption, which responsible moral agents should willingly reduce in order to mitigate global climate change. It considers several mechanisms for doing so, and contends that they may succeed, but only if combined with an explicit recognition and binding commitment that for the foreseeable future, aviation must be a slow-growth or no-growth sector of the world economy.