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A common transcoding operation consists of reducing the file size of a JPEG image to meet bandwidth or device constraints. This can be achieved by reducing its quality factor (QF) or reducing its resolution, or both. In this paper, using the structural similarity (SSIM) index as the quality metric, we present a system capable of estimating the QF and scaling parameters to achieve optimal quality while meeting a device's constraints. We then propose a novel low-complexity JPEG transcoding system which delivers near-optimal quality. The system is capable of predicting the best combination of QF and scaling parameters for a wide range of device constraints and viewing conditions. Although its computational complexity is an order of magnitude smaller than the system providing optimal quality, the proposed system yields quality results very similar to those of the optimal system.