We present an inverse method that uses measurements of the concentration of several tracer variables to find the mixture of source water types that best describes (in a weighted least squares sense) the composition of the water sample. The solution includes two physically realistic constraints: first, that all sources together must sum to 100% and, second, that no source is present in negative amounts. These constraints improve the statistical stability of the solution. The method is particularly valuable in regions involving strong mixing among a relatively large number of source water types. In contrast to conventional TS analysis, more water types can be considered, the assumption of mixing along isopycnals is unnecessary, and sensitivity to errors in individual tracer measurements is reduced by averaging the influence of a larger number of tracers. We demonstrate the method using data from two oceanographic regions. Analysis of summer data from the continental margin off Vancouver Island (British Columbia, Canada) confirms and quantifies the importance of deep upwelling of California Undercurrent water onto the continental shelf. It also identifies localized outer shelf filaments of low-salinity water originating from the Vancouver Island Coastal Current. Finally, we reanalyze the North African data of Tomczak and confirm his interpretation of diapycnal mixing at the frontal boundary between North Atlantic Central Water and South Atlantic Central Water masses. ¿American Geophysical Union 1987