In managing networks of stock holding locations, two approaches to the pooling of inventory have been proposed. Reactive transshipm nts respond to stockouts at a location by moving inventory from elsewhere within the network, while proactive redistribution of stock seeks to minimise the chance of future shocks. This paper is the first to propose a hybrid approach in which transshipments are viewed as an opportunity for stock redistribution. We adopt a quasi-myopic approach to the development of a strongly performing hybrid transshipment policy. Numerical studies which utilise dynamic programming and simulation testify to the benefits of using transshipments proactively. In comparison to a purely reactive approach to transshipment, service levels are improved while a reduction in safety stock levels is achieved. The aggregate costs incurred in managing the system are significantly reduced, especially so for large networks facing high levels of demand.