Agriculture is by far the dominant user of water in the western United States and in nearly all arid regions of the planet. Despite this fact and despite a growing push to rely on price mechanisms for rationalizing water allocation, there are few econometric studies of agricultural water demand that measure its responsiveness to price. Using a unique panel data set of water use at a disaggregated level, this paper estimates the parameters of an agricultural water demand function. The approach incorporates the notion of "jointness" in the farm production function, which postulates that producers choose inputs, outputs and technology simultaneously. Estimation results indicate that the own-price elasticity of water use is in the range [-0.415, -0.275], which includes the indirect effects of water price changes on output and technology choices. The estimation results also provide the first direct measurement of the conservation benefits of investment in precision irrigation technology. Water savings from technology adoption vary widely by crop but can be as high as 50 percent relative to gravity irrigation.