Pinch analysis has been applied to mass exchange network synthesis. Until now, minimum utility targets have existed, but not capital cost targets. Previous work minimised the number of units in a network, but this paper shows that this does not necessarily minimise the capital cost.This paper focuses on the special case of water minimisation. It considers a simple example involving a network of absorption columns which use water to remove sulphur dioxide from a set of gas streams. The paper describes the first known method for targeting the minimum number; of trays in the network, based on a specified 'minimum composition difference'. This is then translated into a capital cost target. An interactive design method is presented which allows the targets to be approached to within 5%.The example is then extended to demonstrate how the targets can be used to trade off capital and operating costs in order to optimise the network before design. A further extension deals with multiple water sources.This work may be extended to other absorbents and generalised to other mass exchange networks.