A new strategy to select the Lagrangian multiplier for nonreference frames is proposed, with the objective to maximize the average PSNR. The selection is based on the observation that nonreference frames should be optimized using a Lagrangian multiplier equivalent to the negative slope of the global R-D curve. This curve is not known a priori and a simple approximation is presented. Further, a new criterion for transform coefficient thresholding is proposed based on the current frame type and Lagrangian optimization. The new scheme is shown to improve the PSNR between 0.35 and 1.12 dB compared to the H.264 Test Model. The average improvement for all sequences is 0.63 dB, or equivalently a bit rate reduction of 11%.