An accurate statistical model of cover images is essential to the success of both steganography and steganalysis. We study the statistics of the full-frame two-dimensional discrete Fourier transform (DFT) coefficients of natural images and show that the independently and identically distributed model with unit exponential distribution is not a sufficiently accurate description of the statistics of normalized image periodograms. Consequently, the stochastic quantization index modulation (QIM) algorithm that aims at preserving this model is detectable in principle. To discriminate the resulted stegoimages from cover images, we train a learning system on them. Building upon a state-of-the-art steganalysis method using the statistical moments of wavelet characteristic functions, we propose new features that are more sensitive to data embedding. The addition of these features significantly improves the steganalyzer's receiver operating characteristic (ROC) curve.