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Many MPEG-2 encoding applications are real-time; this implies that the video signal must be encoded with no significant lookahead. However, there exist non-real-time applications that do enable us to first analyze a video sequence entirely, and, using the analysis results, to optimize a second encoding pass of the same data. One example of such an application is the digital video disk (DVD), which is designed to facilitate a variable-bit-rate (VBR) output stream. In that case, it is possible to let the MPEG-2 encoder produce a video sequence with a constant visual quality over time. This is in contrast to constant-bit-rate (CBR) systems, where the rate is constant but the visual quality varies with the coding difficulty. This paper describes a two-pass encoding system that has as its objective to produce an optimized VBR data stream in a second pass. In a first pass, the video sequence is encoded with CBR, while statistics concerning coding complexity are gathered. Next, the first-pass data is processed to prepare the control parameters for the second pass, which performs the actual VBR compression. In this off-line processing stage, we determine the target number of bits for each picture in the sequence, such that we realize the VBR objective. This means that the available bits are appropriately distributed over the different video segments such that constant visual quality is obtained. To be able to quantify the constant visual quality, perceptual experiments are described and a practical model is fitted to them. Exceptional cases such as scene changes and fades are detected and dealt with appropriately. We also ensure that the second-pass compression process does not violate the decoder buffer boundaries. Finally, the encoding is performed again, but now under control of the processed first-pass data. During the running of this second pass, a run-time bit-production control mechanism monitors the accuracy and validity of the first-pass data, correcting errors in prediction and observing the buffer boundaries. Results are compared to CBR operation.