This discussion paper led to the article with the same title in 'Social Choice and Welfare' (2014), 43, 173-194.
We consider the problem of sharing water among agents located along a river. Each agent has quasi-linear preferences over river water and money, where the benefit of consuming an amount of water is given by a continuous and concave benefit function. A solution to the problem efficiently distributes the river water over the agents and wastes no money. We introduce a number of (independence) axioms to characterize two new and two existing solutions. We apply the solutions to the particular case that every agent has constant marginal benefit of one up to a satiation point and marginal benefit of zero thereafter. In this case we find that two of the solutions (one existing and one new) can be implemented without monetary transfers between the agents.