Swarming peer-to-peer systems play an increasingly instrumental role in Internet content distribution. It is therefore important to better understand how these systems behave in practice. Recent research efforts have looked at various protocol parameters and have measured how they affect system performance and robustness. However, the importance of the strategy based on which peers establish connections has been largely overlooked. This work utilizes extensive simulations to examine the default overlay construction strategy in BitTorrent systems. Based on the results, we identify a critical parameter, the maximum allowable number of outgoing connections at each peer, and evaluate its impact on the robustness of the generated overlay. We find that there is no single optimal value for this parameter using the default strategy. We then propose an alternative strategy that allows certain new peer connection requests to replace existing connections. Further experiments with the new strategy demonstrate that it outperforms the default one for all considered metrics by creating an overlay more robust to churn. Additionally, our proposed strategy exhibits optimal behavior for a well-defined value of the maximum number of outgoing connections, thereby removing the need to set this parameter in an ad-hoc manner.