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In wavelet-based L∞-constrained embedded coding, the bit-stream is truncated at the bit-rate that corresponds to a guaranteed, user-defined distortion bound. The letter analyzes the optimality of embedded deadzone scalar-quantizers for high-rate L∞-constrained scalable wavelet-based image coding. A rate-distortion model applicable to the family of embedded deadzone scalar-quantizers is derived and experimentally validated. Conclusions are drawn regarding the optimal subband-quantizer instantiations. The optimal quantizers are employed in a coding algorithm that retains the coding performance and the flexibility options of wavelet-based codecs while allowing for a fully embedded L∞-oriented bit-stream.