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We consider optimal formulations of spread spectrum watermark embedding where the common requirements of watermarking, such as perceptual closeness of the watermarked image to the cover and detectability of the watermark in the presence of noise and compression, are posed as constraints while one metric pertaining to these requirements is optimized. We propose an algorithmic framework for solving these optimal embedding problems via a multistep feasibility approach that combines projections onto convex sets (POCS) based feasibility watermarking with a bisection parameter search for determining the optimum value of the objective function and the optimum watermarked image. The framework is general and can handle optimal watermark embedding problems with convex and quasi-convex formulations of watermark requirements with assured convergence to the global optimum. The proposed scheme is a natural extension of set-theoretic watermark design and provides a link between convex feasibility and optimization formulations for watermark embedding. We demonstrate a number of optimal watermark embeddings in the proposed framework corresponding to maximal robustness to additive noise, maximal robustness to compression, minimal frequency weighted perceptual distortion, and minimal watermark texture visibility. Experimental results demonstrate that the framework is effective in optimizing the desired characteristic while meeting the constraints. The results also highlight both anticipated and unanticipated competition between the common requirements for watermark embedding.