The number of living donations of human organs, tissues, and cells falls far short of the need. Market-like arrangements to increase donation rates have been proposed, but they are broadly considered unacceptable due to ethical concerns and are therefore not policy relevant in most countries. The purpose of this paper is to explore a different approach to increasing living donations, namely through the use of ethically acceptable compensation of donors. We review the compensation practices in Europe and find a lack of reimbursement of incurred costs and lack of compensation for non-monetary losses, which create disincentives for donation. We draw on a well-known philosophical theory to explain why donors are rarely fully compensated and why many existing proposals to raise donation rates are seen as controversial or even unethical. We present and discuss three categories of compensation with the potential to increase donation rates in an ethically acceptable way.