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We discuss new theoretical and experimental results on the dynamic rate shaping (DRS) approach for transcoding compressed video bitstreams (MPEG-1, MPEG-2, MPEG-4, H.261, as well as JPEG). We analyze the behavior of DRS assuming a first order autoregressive source. We propose a set of low complexity algorithms for both constrained and unconstrained DRS and substantiate the almost-optimal experimental performance of the memoryless algorithm by assuming a first order autoregressive source. By deriving the statistical and rate-distortion characteristics of different components of the interframe rate shaping problem, we offer an explanation as to why the set of optimal breakpoint values for any frame is somewhat invariant to the accumulated motion compensated shaping error from past frames. We also present an extensive experimental study on the various DRS algorithms (causally optimal, memoryless, and rate-based) both in their constrained and generalized forms. The study proves the computational viability of the DRS approach to transcoding and identifies a range of rate shaping ratios for which it is better than requantization, both complexity-wise as well as in performance. This result is significant in that it opens up the way to construct much simpler memoryless algorithms that give minimal penalty in achieved quality, not just for this but possibly other types of algorithms. This is also the very first use of matrix perturbation theory for tracking the spectral behavior of the autocorrelation matrix of the source signal and the motion residual it yields.