Steganography is a technique of embedding information in innocuous data such that only the innocent data is visible. The wavelet transform lends itself to image steganography because it generates a large number of coefficients representing the information in the image. Altering a small set of these coefficients allows embedding of information (payload) into an image (cover) without noticeably altering the original image. We propose a novel, dual-wavelet steganographic technique, using transforms selected such that the transform of the cover image has low sparsity, while the payload transform has high sparsity. Maximizing the sparsity of the payload transform reduces the amount of information embedded in the cover, and minimizing the sparsity of the cover increases the locations that can be altered without significantly altering the image. Making this system effective on any given image pair requires a metric to indicate the best (maximum sparsity) and worst (minimum sparsity) wavelet transforms to use. This paper develops the first stage of this metric, which can predict, averaged across many wavelet families, which of two images will have a higher sparsity. A prototype implementation of the dual-wavelet system as a proof of concept is also developed.