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We recently developed a new benchmark for steganography, underpinned by the square root law of capacity, called Steganographic Fisher Information (SFI). It is related to the multiplicative constant for the square root capacity rate and represents a truly information theoretic measure of asymptotic evidence. Given a very large corpus of covers from which the joint histograms can be estimated, an estimator for SFI was derived in [1], and certain aspects of embedding and detection were compared using this benchmark. In this paper we concentrate on the evidence presented by various spatial-domain embedding operations. We extend the technology of [1] in two ways, to convex combinations of arbitrary so-called independent embedding functions. We then apply the new techniques to estimate, in genuine sets of cover images, the spatial-domain stego noise shape which optimally trades evidence - in terms of asymptotic KL divergence - for capacity. The results suggest that smallest embedding changes are optimal for cover images not exhibiting much noise, and also for cover images with significant saturation, but in noisy images it is superior to embed with more stego noise in fewer locations. © 2009 Springer.