In the absence of kidney markets, alternative institutions for exchanging kidneys have arisen to give donors incentives to donate. I examine thirteen such institutions, and ask whether moral arguments against markets, such as commodification, apply to them or not. I find that most arguments against kidney arguments also argue against these alternative institutions, meaning those arguments are not strong enough to prevent society from using institutions to exchange kidneys. Two arguments that do explain which kidney exchange institutions are socially accepted (...) and which are not are that institutions should not be want-regarding and should not be exploitative.Screening donors to eliminate those with socially unacceptable motives for donation and those who are in a position of being exploited could make kidney markets acceptable, since they would then only be vulnerable to arguments which have not prevented alternative exchange institutions from functioning. (shrink)