A method of water mass analysis is developed which optimizes the use of all information contained in a hydrographic data set by solving an overdetermined linear set of mixing equations. It requires representation of water masses by a finite number of water types and observations from at least as many oceanographic parameters as water types. The procedure to establish the water types, find the correct weights for the parameters, and solve the mixing equations through minimization of the residuals is described in detail. The method is applied to a data set from the eastern Indian Ocean, where Indian Central Water and Australasian Mediterranean Water meet to a produce a strong front in the thermocline. It is shown that although most of the water from the Indonesian archipelago is carried westward north of 11¿S, contributions from the Australasian Mediterranean Water are found as far south as 25¿S, particularly along the Australian shelf as a result of advection with the Leeuwin Current. ¿ American Geophysical Union 1989