Peer-to-Peer systems (P2P systems) have received much attention both in research and in practice. P2P systems consist of autonomous entities, as peers are software artifacts chosen and controlled by humans, or they may be humans themselves, as in social networks. Thus, a peer can choose (a) its action-selection strategy, i.e., how it deals with queries on behalf of others, and (b) its link-selection strategy. In so-called structured P2P systems, a peer typically does not interact directly with another one on the application level, but forwards its queries via intermediate peers. Peers in P2P systems expect some benefit from participating. In particular, they benefit if the system is efficient, i.e., if the payoff of all participants is maximal. Since maintaining contacts incurs costs, having only few contacts is attractive. Consequently, we expect some peers to be deliberately poorly connected (dpc): They hardly have any contacts and hence low maintenance costs. Still, a dpc peer benefits from the network structure, since other peers forward its queries via their contacts. In other words, dpc is a new kind of free riding behavior, namely on the contact level (as opposed to free riding on the action level). Since, from a global perspective, a lower degree of connectivity and a higher forwarding load than necessary result, dpc reduces efficiency. In this article we introduce a formal model to show that in many situations dpc indeed leads to a higher payoff than having many links, i.e., cooperation. Further, we show by means of an economic experiment that humans actually do resort to dpc in network-formation situations. To deal with this situation, we propose an incentive mechanism against dpc. The idea is that participants are more cooperative against peers which obviously are not dpc, compared to other peers. We show the effectiveness of our mechanism with a formal analysis.