The adoption of performance related pay schemes has become increasingly popular in the public sector of several countries. In the UK, the scheme designers favoured collective performance pay with the aim to foster cooperation across offices. The resulting team structure included several offices (subteams) within the same team, defined by the remuneration scheme. In this paper we analyse the strategic interactions across subteams created by a two-level team structure, in order to assess whether rewarding collective performance necessarily promotes cooperation. We show that such team structure creates conflicting incentives to free-ride across and within subteams. Moreover, the relative size of subteams can be a powerful means to deliver incentives when funds for performance rewards are limited. Using data for one of the incentive schemes piloted in the UK, we analyse the role of the target level and of the relative size of subteams on subteams' performance.