Previous works, including adaptive quantizer selection and adaptive coefficient thresholding, have addressed the optimization of a baseline-decodable JPEG coder in a rate-distortion (R-D) sense. In this work, by developing an entropy-constrained quantization framework, we show that these previous works do not fully realize the attainable coding gain, and then formulate a computationally efficient way that attempts to fully realize this gain for baseline-JPEG-decodable systems. Interestingly, we find that the gains obtained using the previous algorithms are almost additive. The framework involves viewing a scalar-quantized system with fixed quantizers as a special type of vector quantizer (VQ), and then to use techniques akin to entropy-constrained vector quantization (ECVQ) to optimize the system. In the JPEG case, a computationally efficient algorithm can be derived, without training, by jointly performing coefficient thresholding, quantizer selection, and Huffman table customization, all compatible with the baseline JPEG syntax. Our algorithm achieves significant R-D improvement over standard JPEG (about 2 dB for typical images) with performance comparable to that of more complex "state-of-the-art" coders. For example, for the Lenna image coded at 1.0 bits per pixel, our JPEG-compatible coder achieves a PSNR of 39.6 dB, which even slightly exceeds the published performance of Shapiro's wavelet coder. Although PSNR does not guarantee subjective performance, our algorithm can be applied with a flexible range of visually-based distortion metrics.