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In the past ten years there have been significant developments in optimization of transcoding parameters on a per-clip rather than per-genre basis. In our recent work we have presented per-clip optimization for the Lagrangian multiplier in Rate controlled compression, which yielded BD-Rate improvements of approximately 2\% across a corpus of videos using HEVC. However, in a video streaming application, the focus is on optimizing the rate/distortion tradeoff at a particular bitrate and not on average across a range of performance. We observed in previous work that a particular multiplier might give BD rate improvements over a certain range of bitrates, but not the entire range. Using different parameters across the range would improve gains overall. Therefore here we present a framework for choosing the best Lagrangian multiplier on a per-operating point basis across a range of bitrates. In effect, we are trying to find the para-optimal gain across bitrate and distortion for a single clip. In the experiments presented we employ direct optimization techniques to estimate this Lagrangian parameter path approximately 2,000 video clips. The clips are primarily from the YouTube-UGC dataset. We optimize both for bitrate savings as well as distortion metrics (PSNR, SSIM).