Large-scale peer-to-peer systems span a wide range of Internet locations. Such diversity can be leveraged to build overlay "detours" to circumvent periods of poor performance on the default path. However, identifying which peers are "good" relay choices in support of such detours is challenging, if one is to avoid incurring an overhead that grows with the size of the peer-to-peer system. This paper proposes and investigates the Earliest Branching Rule (EBR) to perform such a selection. EBR builds on the Earliest Diverging Rule (EDR) that selects relay nodes whose AS path diverges from the default path at the earliest possible point, but calls for monitoring a much smaller number of paths. As a result, it has a much lower overhead. The paper explores the performance and overhead of EBR, and compares them to that of EDR. The results demonstrate that EBR succeeds in selecting good relay nodes with minimum control overhead. Hence, providing a practical solution for dynamically building good overlays in large peer-to-peer systems.