Resilient Packet Ring (RPR) is a recent networking standard developed by the IEEE LAN/MAN working group. RPR is an insertion buffer, dual ring technology, utilizing a back pressure based fairness algorithm to distribute bandwidth when congestion occurs. The fairness algorithm has two modes of operation, called respectively the aggressive and the conservative fairness modes. For some scenarios, the aggressive mode fairness suffers from severe performance deficiencies. In this paper, we propose two novel contributions. The first is a measurement method which enables a node to determine its operating context. The second contribution is a fair rate calculation method, termed the moderate fairness mode, which solves the aggressive mode performance deficiencies while retaining several other properties provided by the aggressive mode fairness. We compare the performance of the moderate fairness mode to that of the aggressive and the conservative modes by simulations, and find that for some scenarios the moderate mode outperforms the aggressive and the conservative modes. For some other scenarios, the convergence time of the moderate mode is somewhat longer than that of the aggressive mode.