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The application of optimal bit allocation in real-time video encoders is a challenging prospect for dependent macroblocks (MBs) where a quantiser is ascribed to each MB within a frame. The operational rate-distortion (R-D) convex hull of INTRA encoded frames may be approximated with a power-law function. However, discontinuities on the surface produce local divergence and therefore an adapting model is proposed that switches between power-law prediction and the bisection method to impose convergence. A performance comparison is made between the bisection method and this adapting model algorithm as applied to the H.263+ video encoder.