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Rings overlay is a class of multi-path routing structure for wireless sensor networks that exploits the broadcast nature of wireless communication to cope with communication failures. While the rings overlay aims to create multiple propagation paths for sensor nodes to transport data, the sensor nodes in the ring next to the base station inherently have only a single propagation path to the base station and their data remain to be transported by single path routing. In this paper, we propose and analyze an enhanced relay scheme for improving the robustness of sensor data collection through the rings overlay. The objective is to let all sensor nodes in the ring next to the base station to benefit from multi-path routing without sacrificing energy efficiency. Analytical and experimental results show that compared with the original relay scheme, the proposed enhanced relay scheme significantly improves the robustness of sensor data collection through the rings overlay.