Abstract 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.