In this paper the Burtless and Hausman model is used to estimate water demand in Salatiga, Indonesia. Other statistical models, as OLS and IV, are found to be inappropiate. A topic, which does not seem to appear in previous studies, is the fact that the density function of the loglikelihood can be made arbitrary high if observations are located exactly on a kink of the budget constraint. To avoid this problem, a discretization technique is used to work with genuine probabilities. The unconditional distribution of water demand is explored with parametric and semiparametric techniques. An important conclusion is that the distribution of water demand is not unimodal and that data are clustered aroundkinks. Main estimation results are a price elasticity of approximately -1.2 and an income elasticity of 0.05. Price and income elasticities are mutually dependent. The estimated model is finally used to investigate consequences for social welfare when a uniform price level is chosen. It is argued that without loss of total welfare, the complex rate structure can be replaced by a uniform marginal price.