The increasing popularity of increasing block tariffs (IBT) for water is reflected in Portugal by a virtually universal implementation for residential use. IBT are often supported as a good tool for achieving the goals of equity, water conservation and revenue neutrality but seldom have they been grounded on efficiency justifications. We test the conditions derived by Roseta-Palma and Monteiro (2008) for IBT to be a second-best pricing practice under water scarcity and budget balancing constraints, when consumers are heterogeneous and the fixed charge is only allowed to cover fixed costs. Because, in these conditions, the choice of tariff schedule design is dependent on the price-elasticity of demand and the way it varies with consumption levels, we estimate the Portuguese residential water demand and show that the resulting recommended tariff schedule hinges crucially on the choice of functional form. After the proper specification test, a choice between a semilogarithmic lin-log and a double-log specifications is left undecided, which does not prove the superiority of IBT, but also does not enable its dismissal. Besides the usual determinants found in the prolific residential water demand estimation literature we find that the proportion of seasonally inhabited dwellings and a reduced water quality on delivery can have a significant negative influence on the amount of water households consume.