We show that scale-free topologies have a positive impact on the performance of gossiping algorithms in peer-to-peer overlay networks. This result is important in the context of ad hoc networks, where each node participates in controlling the network topology. Our study shows that, when combined with such topologies, typical gossiping algorithms tend to require fewer messages and experience smaller latency than when combined with other topologies, such as rings or grids. This suggests that the topology control scheme should aim at producing an overlay network that exhibits scale-free characteristics.