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In the perceptually transparent coding of images, we use representation and quantization strategies that exploit properties of human perception to obtain an approximate digital image indistinguishable from the original. This image is then encoded in an error free manner. The resulting coders have better performance than error free coding for a comparable quality. Further, by considering changes to images that do not produce perceptible distortion, we identify image characteristics onerous for the encoder, but perceptually unimportant. Once such characteristic is the typical noise level, often imperceptible, encountered in still images. Thus, we consider adaptive noise removal to improve coder performance, without perceptible degradation of quality. In this paper, several elements contribute to coding efficiency while preserving image quality: adaptive noise removal, additive decomposition of the image with a high activity remainder, coarse quantization of the remainder, progressive representation of the remainder, using bilinear or directional interpolation methods, and efficient encoding of the sparse remainder. The overall coding performance improvement due to noise removal and the use of a progressive code is about 18%, as compared to our previous results for perceptually transparent coders. The compression ratio for a set of nine test images is 3.72 for no perceptible loss of quality.