This paper presents a new method for targeting maximum water reuse in processing systems. Two cases are considered. In the first case, the mass transfer is modelled in terms of a fixed mass load. This leads to a problem which can be solved as a non-linear optimization problem. Ln the second case, the mass transfer is modelled in terms of a fixed outlet concentration. This leads to a problem which can be solved as a linear optimization problem. In practice, many water-using operations will call for the mass exchange characteristics of some contaminants to be modelled by fixed mass load and others to be modelled by fixed outlet concentration, leading overall to a non-linear problem. To overcome the difficulties associated with non-linear optimization, a combined approach is presented in which the linear model is used to provide an initialization for non-linear optimization. The new method has also been combined with a previously published graphical approach to provide a representation which incorporates all constraints, not only concentration, but also flowrate constraints and forbidden matches, etc.