The contribution of this paper is two-fold. First, we describe an improved version of a blind steganalysis method previously proposed by Holotyak et al. and compare it to current state-of-the-art blind steganalyzers. The features for the blind classifier are calculated in the wavelet domain as higher-order absolute moments of the noise residual. This method clearly shows the benefit of calculating the features from the noise residual because it increases the features' sensitivity to embedding, which leads to improved detection results. Second, using this detection engine, we attempt to answer some fundamental questions, such as "how much can we improve the reliability of steganalysis given certain a priori side-information about the image source?" Moreover, we experimentally compare the security of three steganographic schemes for images stored in a raster format - (1) pseudo-random ±1 embedding using ternary matrix embedding, (2) spatially adaptive ternary ±1 embedding, and (3) perturbed quantization while converting a 16-bit per channel image to an 8-bit gray scale image.