A model of residential water demand is presented, explicitly considering a non-zero share of water consumption that is insensitive to price. The demand equation, based on the Stone-Geary utility function, includes a threshold of water independent of prices and a quantity that can adapt instantaneously to price changes. First, the threshold is assumed constant, while it is allowed to vary, in a second model, according to past levels of consumption, a proxy for households' water-using equipment and habits. A measure of the depreciation rate of habits is derived and the effectiveness of price and non-price conservation measures are compared. The results provide useful policy recommendations for the studied case of Seville (Spain).