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In this work, we combine the recently proposed GLICBAWLS (grey level image compression by adaptive weighted least squares) lossless image compression algorithm with integer-to-integer wavelet transforms to create a resolution-progressive algorithm capable of lossless quality. We find that modifying the prediction window to exploit inter-scale redundancy is quite helpful at some points in the processing but not universally. To evaluate the effectiveness of our algorithm, we consider the compression of both 16-bit digital elevation maps (DEMs) and 8-bit images. For purposes of comparison, we also apply a lossless version of SPIHT to the same data sets. For higher resolution DEMs, we find that GLICBAWLS+wavelets is superior while for lower resolution DEMs, SPIHT is the better choice.