An important, but under-researched, question in relation to policies funding networks of innovators is:what kind of innovation networks should be supported, if the policy objective is not just to sponsor successful innovation projects, but also to encourage the participants to form networks with desirable characteristics? Focusing on a set of policy programmes implemented by the regional government of Tuscany, in Italy, between 2002 and 2008, aimed at funding networks of collaborating organisations, we investigate whether the imposition of requirements on the composition of the networks that would be eligible for funding -in particular, the demand that networks should comply with minimum size and heterogeneity thresholds -influenced the participants' networking behaviour in the context of successive policy interventions. Our results show that these requirements immediately affected the size and composition of the project networks that applied for funding, although not always in the intended direction. However, these effects did not extend to the successive periods, when those requirements were no longer in force. This suggests that the imposition of policy requirements, per se, is unlikely to induce persistent changes in organizations' networking behaviour. Other approaches such as implementing outreach actions in order to encourage new organisations to participate in existing innovation networks and to form new ones, and additional measures designed to foster learning opportunities for the participants, might be more effective tools to influence the networking behaviour of participating organisations.