The performance of quantization-based data hiding methods is commonly analyzed by assuming a flat probability density function for the host signal, i.e. uniform inside each quantization cell and
with its variance large enough to assuming that all the centroids occur with equal probability. This paper comes to fill a gap in watermarking theory, analyzing the exact performance of the Scalar Costa Scheme (SCS) facing additive Gaussian attacks when the former approximation is not valid, thus taking into account the host statistics. The accomplished analysis reveals that the true performance of such a scheme for an optimal selection of its parameters and low watermark to noise ratios (WNR) is never worse than that of classical spread-spectrum-based methods, in terms of achievable rate and probability of error, as it was thought so far. The reduction of SCS to a two-centroid problem allows the derivation of theoretical expressions which characterize its behavior for small WNR's, showing interesting connections with spread-spectrum (SS) and the Improved Spread Spectrum (ISS) method. Furthermore, we show that, in contrast to the results reported until now, the use of pseudorandom dithering in SCS-based schemes can have a negative impact in performance. Performance losses are also reported for the case in which a modulo reduction is undertaken prior to decoding. The usefulness of these results is shown in the computation of the exact performance in projected domains.